1.
String theory
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In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. It describes how strings propagate through space and interact with each other. On distance scales larger than the scale, a string looks just like an ordinary particle, with its mass, charge. In string theory, one of the vibrational states of the string corresponds to the graviton. Thus string theory is a theory of quantum gravity, String theory is a broad and varied subject that attempts to address a number of deep questions of fundamental physics. Despite much work on problems, it is not known to what extent string theory describes the real world or how much freedom the theory allows to choose the details. String theory was first studied in the late 1960s as a theory of the nuclear force. Subsequently, it was realized that the properties that made string theory unsuitable as a theory of nuclear physics made it a promising candidate for a quantum theory of gravity. The earliest version of string theory, bosonic string theory, incorporated only the class of known as bosons. It later developed into superstring theory, which posits a connection called supersymmetry between bosons and the class of particles called fermions. In late 1997, theorists discovered an important relationship called the AdS/CFT correspondence, one of the challenges of string theory is that the full theory does not have a satisfactory definition in all circumstances. Another issue is that the theory is thought to describe an enormous landscape of possible universes, and these issues have led some in the community to criticize these approaches to physics and question the value of continued research on string theory unification. In the twentieth century, two theoretical frameworks emerged for formulating the laws of physics, one of these frameworks was Albert Einsteins general theory of relativity, a theory that explains the force of gravity and the structure of space and time. The other was quantum mechanics, a different formalism for describing physical phenomena using probability. In spite of successes, there are still many problems that remain to be solved. One of the deepest problems in physics is the problem of quantum gravity. The general theory of relativity is formulated within the framework of classical physics, in addition to the problem of developing a consistent theory of quantum gravity, there are many other fundamental problems in the physics of atomic nuclei, black holes, and the early universe. String theory is a framework that attempts to address these questions
2.
String vibration
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A vibration in a string is a wave. Resonance causes a string to produce a sound with constant frequency. If the length or tension of the string is correctly adjusted, vibrating strings are the basis of string instruments such as guitars, cellos, and pianos. Let Δ x be the length of a piece of string, m its mass, and μ its linear density. If the horizontal component of tension in the string is a constant, T, if both angles are small, then the tensions on either side are equal and the net horizontal force is zero. This is the equation for y, and the coefficient of the second time derivative term is equal to v −2, thus v = T μ. Once the speed of propagation is known, the frequency of the produced by the string can be calculated. The speed of propagation of a wave is equal to the wavelength λ divided by the period τ, or multiplied by the frequency f, v = λ τ = λ f. If the length of the string is L, the harmonic is the one produced by the vibration whose nodes are the two ends of the string, so L is half of the wavelength of the fundamental harmonic. Hence one obtains Mersennes laws, f = v 2 L =12 L T μ where T is the tension, μ is the linear density, and L is the length of the vibrating part of the string. This effect is called the effect, and the rate at which the string seems to vibrate is the difference between the frequency of the string and the refresh rate of the screen. The same can happen with a fluorescent lamp, at a rate that is the difference between the frequency of the string and the frequency of the alternating current. In daylight and other non-oscillating light sources, this effect does not occur and the string appears still but thicker, a similar but more controllable effect can be obtained using a stroboscope. This device allows matching the frequency of the flash lamp to the frequency of vibration of the string. In a dark room, this shows the waveform. Otherwise, one can use bending or, perhaps more easily, by adjusting the machine heads, to obtain the same, or a multiple, of the AC frequency to achieve the same effect. For example, in the case of a guitar, the 6th string pressed to the third gives a G at 97.999 Hz. A slight adjustment can alter it to 100 Hz, exactly one octave above the current frequency in Europe and most countries in Africa
3.
Brane
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In string theory and related theories such as supergravity theories, a brane is a physical object that generalizes the notion of a point particle to higher dimensions. Branes are dynamical objects which can propagate through spacetime according to the rules of quantum mechanics and they have mass and can have other attributes such as charge. Mathematically, branes can be represented within categories, and are studied in mathematics for insight into homological mirror symmetry. A point particle can be viewed as a brane of dimension zero, in addition to point particles and strings, it is possible to consider higher-dimensional branes. In dimension p, these are called p-branes, the word brane comes from the word membrane which refers to a two-dimensional brane. A p-brane sweeps out a volume in spacetime called its worldvolume. Physicists often study fields analogous to the field, which live on the worldvolume of a brane. In string theory, a string may be open or closed, D-branes are an important class of branes that arise when one considers open strings. As an open string propagates through spacetime, its endpoints are required to lie on a D-brane, the letter D in D-brane refers to Dirichlet boundary condition, which the D-brane satisfies. This connection has led to important insights into gauge theory and quantum field theory, mathematically, branes can be described using the notion of a category. This is a structure consisting of objects, and for any pair of objects. In most examples, the objects are structures and the morphisms are functions between these structures. One can also consider categories where the objects are D-branes and the morphisms between two branes α and β are states of open strings stretched between α and β. Intuitively, one can think of a submanifold as a surface embedded inside of a Calabi–Yau manifold, in mathematical language, the category having these branes as its objects is known as the derived category of coherent sheaves on the Calabi–Yau. In another version of string theory called the topological A-model, the D-branes can again be viewed as submanifolds of a Calabi–Yau manifold, roughly speaking, they are what mathematicians call special Lagrangian submanifolds. This means among other things that they have half the dimension of the space in which they sit, the category having these branes as its objects is called the Fukaya category. On the other hand, the Fukaya category is constructed using symplectic geometry, symplectic geometry studies spaces equipped with a symplectic form, a mathematical tool that can be used to compute area in two-dimensional examples. This equivalence provides a bridge between two branches of geometry, namely complex and symplectic geometry. M. H
4.
Bosonic string theory
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Bosonic string theory is the original version of string theory, developed in the late 1960s. It is so called because it only contains bosons in the spectrum, in the 1980s, supersymmetry was discovered in the context of string theory, and a new version of string theory called superstring theory became the real focus. Although bosonic string theory has many features, it falls short as a viable physical model in two significant areas. First, it only the existence of bosons whereas many physical particles are fermions. Second, it predicts the existence of a mode of the string with imaginary mass, in addition, bosonic string theory in a general spacetime dimension displays inconsistencies due to the conformal anomaly. But, as was first noticed by Claud Lovelace, in a spacetime of 26 dimensions, the dimension for the theory. This would leave only the four dimensions of spacetime visible to low energy experiments. The existence of a dimension where the anomaly cancels is a general feature of all string theories. There are four possible bosonic string theories, depending on whether open strings are allowed, recall that a theory of open strings also must include closed strings, open strings can be thought as having their endpoints fixed on a D25-brane that fills all of spacetime. A specific orientation of the means that only interaction corresponding to an orientable worldsheet are allowed. A sketch of the spectra of the four theories is as follows, Note that all four theories have a negative energy tachyon. The rest of this article applies to the closed, oriented theory, corresponding to borderless, G is the metric on the target spacetime, which is usually taken to be the Minkowski metric in the perturbative theory. Under a Wick rotation, this is brought to a Euclidean metric G μ ν = δ μ ν, M is the worldsheet as a topological manifold parametrized by the ξ coordinates. T is the tension and related to the Regge slope as T =12 π α ′. I0 has diffeomorphism and Weyl invariance, a normalization factor N is introduced to compensate overcounting from symmetries. While the computation of the partition function correspond to the cosmological constant, the symmetry group of the action actually reduces drastically the integration space to a finite dimensional manifold. One still has to quotient away diffeomorphisms, the fundamental problem of perturbative bosonic strings therefore becomes the parametrization of Moduli space, which is non-trivial for genus h ≥4. At tree-level, corresponding to genus 0, the cosmological constant vanishes, Z0 =0
5.
Superstring theory
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Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modelling them as vibrations of tiny supersymmetric strings. Since the second superstring revolution, the five superstring theories are regarded as different limits of a single theory tentatively called M-theory, the development of a quantum field theory of a force invariably results in infinite possibilities. Development of quantum theory of gravity therefore requires different means than those used for the other forces, according to the theory, the fundamental constituents of reality are strings of the Planck length that vibrate at resonant frequencies. Every string, in theory, has a resonance, or harmonic. Different harmonics determine different fundamental particles, the tension in a string is on the order of the Planck force. The graviton, for example, is predicted by the theory to be a string with wave amplitude zero, since its beginnings in late sixties, the theory was developed through several decades of intense research and combined effort of numerous scientists. It has developed into a broad and varied subject with connections to quantum gravity, particle and condensed matter physics, cosmology, superstring theory is based on supersymmetry. No supersymmetric particles have been discovered and recent research at LHC, for instance, the mass constraint of the Minimal Supersymmetric Standard Model squarks has been up to 1.1 TeV, and gluinos up to 500 GeV. No report on suggesting large extra dimensions has been delivered from LHC, there have been no principles so far to limit the number of vacua in the concept of a landscape of vacua. Our physical space is observed to have three spatial dimensions and, along with time, is a boundless four-dimensional continuum known as spacetime. However, nothing prevents a theory from including more than 4 dimensions, in the case of string theory, consistency requires spacetime to have 10 dimensions. If the extra dimensions are compactified, then the six dimensions must be in the form of a Calabi–Yau manifold. Within the more complete framework of M-theory, they would have to form of a G2 manifold. Calabi-Yaus are interesting mathematical spaces in their own right, a particular exact symmetry of string/M-theory called T-duality, has led to the discovery of equivalences between different Calabi-Yaus called Mirror Symmetry. Superstring theory is not the first theory to propose extra spatial dimensions and it can be seen as building upon the Kaluza–Klein theory, which proposed a 4+1-dimensional theory of gravity. When compactified on a circle, the gravity in the extra dimension precisely describes electromagnetism from the perspective of the 3 remaining large space dimensions, also, to obtain a consistent, fundamental, quantum theory requires the upgrade to string theory—not just the extra dimensions. Theoretical physicists were troubled by the existence of five separate superstring theories, the five consistent superstring theories are, The type I string has one supersymmetry in the ten-dimensional sense. This theory is special in the sense that it is based on unoriented open and closed strings, the type II string theories have two supersymmetries in the ten-dimensional sense
6.
Type I string theory
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In theoretical physics, type I string theory is one of five consistent supersymmetric string theories in ten dimensions. It is the one whose strings are unoriented and which contains not only closed strings. At low energies, type I string theory is described by the N=1 supergravity in ten dimensions coupled to the SO supersymmetric Yang–Mills theory, the discovery in 1984 by Michael Green and John H. Schwarz that anomalies in type I string theory cancel sparked the first superstring revolution. It opened the way to the construction of new classes of string spectra with or without supersymmetry. Joseph Polchinskis work on D-branes provided an interpretation for these results in terms of extended objects. In the 1990s it was first argued by Edward Witten that type I string theory with the coupling constant g is equivalent to the SO heterotic string with the coupling 1 / g. This equivalence is known as S-duality, E. Witten, String theory dynamics in various dimensions, Nucl. J. Polchinski, S. Chaudhuri and C. V, angelantonj and A. Sagnotti, Open strings, Phys
7.
Type II string theory
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In theoretical physics, type II string theory is a unified term that includes both type IIA strings and type IIB strings theories. Type II string theory accounts for two of the five consistent superstring theories in ten dimensions, both theories have the maximal amount of supersymmetry — namely 32 supercharges — in ten dimensions. Both theories are based on oriented closed strings, on the worldsheet, they differ only in the choice of GSO projection. In the 1990s it was realized by Edward Witten that the limit of type IIA string theory in which the string coupling goes to infinity becomes a new 11-dimensional theory called M-theory. The mathematical treatment of type IIA string theory belongs to symplectic topology and algebraic geometry, in the 1990s it was realized that type II string theory with the string coupling constant g is equivalent to the same theory with the coupling 1/g. This equivalence is known as S-duality, orientifold of type IIB string theory leads to type I string theory. The mathematical treatment of type IIB string theory belongs to algebraic geometry, specifically the theory of complex structures originally studied by Kunihiko Kodaira. In the late 1980s, it was realized that type IIA string theory is related to type IIB string theory by T-duality, superstring theory Type I string Heterotic string
8.
S-duality
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In theoretical physics, S-duality is an equivalence of two physical theories, which may be either quantum field theories or string theories. S-duality is useful for doing calculations in physics because it relates a theory in which calculations are difficult to a theory in which they are easier. In quantum field theory, S-duality generalizes a well known fact from classical electrodynamics, one of the earliest known examples of S-duality in quantum field theory is Montonen–Olive duality which relates two versions of a quantum field theory called N =4 supersymmetric Yang–Mills theory. Recent work of Anton Kapustin and Edward Witten suggests that Montonen–Olive duality is related to a research program in mathematics called the geometric Langlands program. Another realization of S-duality in quantum theory is Seiberg duality. There are also examples of S-duality in string theory. The existence of these dualities implies that seemingly different formulations of string theory are actually physically equivalent. This led to the realization, in the mid-1990s, that all of the five consistent superstring theories are just different limiting cases of a single theory called M-theory. In quantum field theory and string theory, a constant is a number that controls the strength of interactions in the theory. Similarly, the strength of the force is described by a coupling constant. To compute observable quantities in field theory or string theory. In order for such an expression to make sense, the constant must be less than 1 so that the higher powers of g become negligibly small. If the coupling constant is not less than 1, then the terms of this sum will grow larger and larger, in this case the theory is said to be strongly coupled, and one cannot use perturbation theory to make predictions. For certain theories, S-duality provides a way of doing computations at strong coupling by translating these computations into different computations in a weakly coupled theory, S-duality is a particular example of a general notion of duality in physics. The term duality refers to a situation where two different physical systems turn out to be equivalent in a nontrivial way. If two theories are related by a duality, it means that one theory can be transformed in some way so that it ends up looking just like the other theory, the two theories are then said to be dual to one another under the transformation. Put differently, the two theories are different descriptions of the same phenomena. S-duality is useful because it relates a theory with coupling constant g to an equivalent theory with coupling constant 1 / g, thus it relates a strongly coupled theory to a weakly coupled theory
9.
T-duality
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In theoretical physics, T-duality is an equivalence of two physical theories, which may be either quantum field theories or string theories. The two theories are equivalent in the sense that all observable quantities in one description are identified with quantities in the dual description. For example, momentum in one description takes discrete values and is equal to the number of times the string winds around the circle in the dual description, the idea of T-duality can be extended to more complicated theories, including superstring theories. The existence of these dualities implies that seemingly different superstring theories are actually physically equivalent and this led to the realization, in the mid-1990s, that all of the five consistent superstring theories are just different limiting cases of a single eleven-dimensional theory called M-theory. In general, T-duality relates two theories with different spacetime geometries, in this way, T-duality suggests a possible scenario in which the classical notions of geometry break down in a theory of Planck scale physics. The geometric relationships suggested by T-duality are also important in pure mathematics, T-duality is a particular example of a general notion of duality in physics. The term duality refers to a situation where two different physical systems turn out to be equivalent in a nontrivial way. If two theories are related by a duality, it means that one theory can be transformed in some way so that it ends up looking just like the other theory, the two theories are then said to be dual to one another under the transformation. Put differently, the two theories are different descriptions of the same phenomena. Like many of the dualities studied in physics, T-duality was discovered in the context of string theory. In string theory, particles are modeled not as zero-dimensional points, the physics of strings can be studied in various numbers of dimensions. In addition to three dimensions from everyday experience, string theories may include one or more compact dimensions which are curled up into circles. A standard analogy for this is to consider multidimensional object such as a garden hose, if the hose is viewed from a sufficient distance, it appears to have only one dimension, its length. However, as one approaches the hose, one discovers that it contains a second dimension, thus, an ant crawling inside it would move in two dimensions. Such extra dimensions are important in T-duality, which relates a theory in which strings propagate on a circle of some radius R to a theory in which strings propagate on a circle of radius 1 / R. In mathematics, the number of a curve in the plane around a given point is an integer representing the total number of times that curve travels counterclockwise around the point. The notion of winding number is important in the description of T-duality where it is used to measure the winding of strings around compact extra dimensions. For example, the image below shows examples of curves in the plane
10.
M-theory
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M-theory is a theory in physics that unifies all consistent versions of superstring theory. The existence of such a theory was first conjectured by Edward Witten at a string theory conference at the University of Southern California in the spring of 1995, Wittens announcement initiated a flurry of research activity known as the second superstring revolution. Prior to Wittens announcement, string theorists had identified five versions of superstring theory, although these theories appeared, at first, to be very different, work by several physicists showed that the theories were related in intricate and nontrivial ways. In particular, physicists found that apparently distinct theories could be unified by mathematical transformations called S-duality and T-duality, Wittens conjecture was based in part on the existence of these dualities and in part on the relationship of the string theories to a field theory called eleven-dimensional supergravity. Modern attempts to formulate M-theory are typically based on theory or the AdS/CFT correspondence. Investigations of the structure of M-theory have spawned important theoretical results in physics and mathematics. More speculatively, M-theory may provide a framework for developing a theory of all of the fundamental forces of nature. One of the deepest problems in physics is the problem of quantum gravity. The current understanding of gravity is based on Albert Einsteins general theory of relativity, however, nongravitational forces are described within the framework of quantum mechanics, a radically different formalism for describing physical phenomena based on probability. String theory is a framework that attempts to reconcile gravity. In string theory, the particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how strings propagate through space and interact with each other, in a given version of string theory, there is only one kind of string, which may look like a small loop or segment of ordinary string, and it can vibrate in different ways. On distance scales larger than the scale, a string will look just like an ordinary particle, with its mass, charge. In this way, all of the different elementary particles may be viewed as vibrating strings, one of the vibrational states of a string gives rise to the graviton, a quantum mechanical particle that carries gravitational force. There are several versions of string theory, type I, type IIA, type IIB, the different theories allow different types of strings, and the particles that arise at low energies exhibit different symmetries. For example, the type I theory includes both open strings and closed strings, while types IIA and IIB include only closed strings, each of these five string theories arises as a special limiting case of M-theory. This theory, like its string theory predecessors, is an example of a theory of gravity. It describes a force just like the familiar gravitational force subject to the rules of quantum mechanics, in everyday life, there are three familiar dimensions of space, height, width and depth
11.
AdS/CFT correspondence
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On one side are anti-de Sitter spaces which are used in theories of quantum gravity, formulated in terms of string theory or M-theory. On the other side of the correspondence are conformal field theories which are quantum field theories, the duality represents a major advance in our understanding of string theory and quantum gravity. It also provides a toolkit for studying strongly coupled quantum field theories. This fact has been used to study aspects of nuclear. The AdS/CFT correspondence was first proposed by Juan Maldacena in late 1997, important aspects of the correspondence were elaborated in articles by Steven Gubser, Igor Klebanov, and Alexander Markovich Polyakov, and by Edward Witten. By 2015, Maldacenas article had over 10,000 citations and our current understanding of gravity is based on Albert Einsteins general theory of relativity. Formulated in 1915, general relativity explains gravity in terms of the geometry of space and time and it is formulated in the language of classical physics developed by physicists such as Isaac Newton and James Clerk Maxwell. The other nongravitational forces are explained in the framework of quantum mechanics, developed in the first half of the twentieth century by a number of different physicists, quantum mechanics provides a radically different way of describing physical phenomena based on probability. Quantum gravity is the branch of physics that seeks to describe gravity using the principles of quantum mechanics, currently, the most popular approach to quantum gravity is string theory, which models elementary particles not as zero-dimensional points but as one-dimensional objects called strings. In the AdS/CFT correspondence, one typically considers theories of quantum gravity derived from string theory or its modern extension, in everyday life, there are three familiar dimensions of space, and there is one dimension of time. Thus, in the language of physics, one says that spacetime is four-dimensional. The quantum gravity theories appearing in the AdS/CFT correspondence are typically obtained from string and this produces a theory in which spacetime has effectively a lower number of dimensions and the extra dimensions are curled up into circles. A standard analogy for compactification is to consider an object such as a garden hose. Thus, an ant crawling inside it would move in two dimensions, the application of quantum mechanics to physical objects such as the electromagnetic field, which are extended in space and time, is known as quantum field theory. In particle physics, quantum field theories form the basis for our understanding of elementary particles, quantum field theories are also used throughout condensed matter physics to model particle-like objects called quasiparticles. In the AdS/CFT correspondence, one considers, in addition to a theory of quantum gravity and this is a particularly symmetric and mathematically well behaved type of quantum field theory. In the AdS/CFT correspondence, one considers string theory or M-theory on an anti-de Sitter background and this means that the geometry of spacetime is described in terms of a certain vacuum solution of Einsteins equation called anti-de Sitter space. It is closely related to space, which can be viewed as a disk as illustrated on the right
12.
String phenomenology
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String phenomenology is a branch of theoretical physics that attempts to construct realistic or semi-realistic models of particle physics based on string theory. The term realistic is usually taken to mean that the low limit of string theory yields a model which bears a resemblance to the Minimal Supersymmetric Standard Model. String cosmology String theory landscape Candelas, Philip, Horowitz, Gary, Strominger, Andrew, Witten, Edward
13.
String cosmology
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String cosmology is a relatively new field that tries to apply equations of string theory to solve the questions of early cosmology. A related area of study is brane cosmology, the idea is related to a property of the bosonic string in a curve background, better known as nonlinear sigma model. As this model has conformal invariance and this must be kept to have a quantum field theory. While Einstein equations seem to appear out of place, nevertheless this result is surely striking showing as a background two-dimensional model could produce higher-dimensional physics. An interesting point here is that such a theory can be formulated without a requirement of criticality at 26 dimensions for consistency as happens on a flat background. This is a hint that the underlying physics of Einstein equations could be described by an effective two-dimensional conformal field theory. Indeed, the fact that we have evidence for a universe is an important support to string cosmology. In the evolution of the universe, after the inflationary phase, a smooth transition is expected between these two different phases. String cosmology appears to have difficulties in explaining this transition and this is known in literature as the graceful exit problem. An inflationary cosmology implies the presence of a field that drives inflation. In string cosmology, this arises from the so-called dilaton field and this is a scalar term entering into the description of the bosonic string that produces a scalar field term into the effective theory at low energies. The corresponding equations resemble those of a Brans–Dicke theory, analysis has been worked out from a critical number of dimension down to four. In general one gets Friedmann equations in an number of dimensions. The other way round is to assume that a number of dimensions is compactified producing an effective four-dimensional theory to work with. Such a theory is a typical Kaluza–Klein theory with a set of scalar fields arising from compactified dimensions and this section presents some of the relevant equations entering into string cosmology. The indices a, b range over 1,2, and μ, ν over 1, …, D, a further antisymmetric field could be added. This is generally considered when one wants this action generating a potential for inflation, otherwise, a generic potential is inserted by hand, as well as a cosmological constant. The above string action has a conformal invariance and this is a property of a two dimensional Riemannian manifold
14.
String theory landscape
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The string theory landscape refers to the huge number of possible false vacua in string theory. In string theory the number of false vacua is thought to be somewhere between 1010 to 10500, the large number of possibilities arises from different choices of Calabi–Yau manifolds and different values of generalized magnetic fluxes over different homology cycles. If one assumes that there is no structure in the space of vacua, in 1987, Steven Weinberg proposed that the observed value of the cosmological constant was so small because it is impossible for life to occur in a universe with a much larger cosmological constant. In order to implement this idea in a physical theory. This has been realized in the context of eternal inflation, Weinberg attempted to predict the magnitude of the cosmological constant based on probabilistic arguments. Other attempts have been made to apply similar reasoning to models of particle physics and these probabilistic arguments are the most controversial aspect of the landscape. The function P s e l e c t i o n is completely unknown, simplified criteria must be used as a proxy for the number of observers. Moreover, it may never be possible to compute it for parameters radically different from those of the observable universe. Tegmark et al. have recently considered these objections and proposed a simplified anthropic scenario for axion dark matter in which they argue that the first two of these problems do not apply, vilenkin and collaborators have proposed a consistent way to define the probabilities for a given vacuum. Prominent proponents of the idea include Andrei Linde, Sir Martin Rees and especially Leonard Susskind, opponents, such as David Gross, suggest that the idea is inherently unscientific, unfalsifiable or premature. A famous debate on the landscape of string theory is the Smolin–Susskind debate on the merits of the landscape. The term landscape comes from evolutionary biology and was first applied to cosmology by Lee Smolin in his book and it was first used in the context of string theory by Susskind. There are several books about the anthropic principle in cosmology. The authors of two physics blogs are opposed to use of the anthropic principle. Extra dimensions Compactification String landscape, moduli stabilization, flux vacua, flux compactification on arxiv. org Cvetič, Mirjam, García-Etxebarria, Iñaki, Halverson, on the computation of non-perturbative effective potentials in the string theory landscape
15.
Mirror symmetry (string theory)
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In algebraic geometry and theoretical physics, mirror symmetry is a relationship between geometric objects called Calabi–Yau manifolds. The term refers to a situation where two Calabi–Yau manifolds look very different geometrically but are equivalent when employed as extra dimensions of string theory. Mirror symmetry was originally discovered by physicists, candelas and his collaborators showed that mirror symmetry could be used to count rational curves on a Calabi–Yau manifold, thus solving a longstanding problem. Today mirror symmetry is a research topic in pure mathematics. Major approaches to mirror symmetry include the mirror symmetry program of Maxim Kontsevich and the SYZ conjecture of Andrew Strominger, Shing-Tung Yau. In physics, string theory is a framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. These strings look like small segments or loops of ordinary string, String theory describes how strings propagate through space and interact with each other. On distance scales larger than the scale, a string will look just like an ordinary particle, with its mass, charge. Splitting and recombination of strings correspond to particle emission and absorption, there are notable differences between the world described by string theory and the everyday world. In everyday life, there are three dimensions of space, and there is one dimension of time. Thus, in the language of physics, one says that spacetime is four-dimensional. One of the features of string theory is that it requires extra dimensions of spacetime for its mathematical consistency. One of the goals of current research in string theory is to develop models in which the strings represent particles observed in high energy physics experiments. In the limit where these curled up dimensions become very small, a standard analogy for this is to consider a multidimensional object such as a garden hose. If the hose is viewed from a sufficient distance, it appears to have one dimension. However, as one approaches the hose, one discovers that it contains a second dimension, thus, an ant crawling on the surface of the hose would move in two dimensions. Compactification can be used to construct models in which spacetime is effectively four-dimensional, however, not every way of compactifying the extra dimensions produces a model with the right properties to describe nature. In a viable model of physics, the compact extra dimensions must be shaped like a Calabi–Yau manifold
16.
Monstrous moonshine
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In mathematics, monstrous moonshine, or moonshine theory, is the unexpected connection between the monster group M and modular functions, in particular, the j function. The term was coined by John Conway and Simon P. Norton in 1979 and this vertex operator algebra is commonly interpreted as a structure underlying a conformal field theory, allowing physics to form a bridge between two mathematical areas. Let r n =1,196883,21296876,842609326,18538750076,19360062527,293553734298 and he won the Fields Medal in 1998 in part for his solution of the conjecture. The Frenkel–Lepowsky–Meurman construction starts with two tools, The construction of a lattice vertex operator algebra VL for an even lattice L of rank n. In physical terms, this is the chiral algebra for a bosonic string compactified on a torus Rn/L and it can be described roughly as the tensor product of the group ring of L with the oscillator representation in n dimensions. For the case in question, one sets L to be the Leech lattice, in physical terms, this describes a bosonic string propagating on a quotient orbifold. The construction of Frenkel–Lepowsky–Meurman was the first time appeared in conformal field theory. Attached to the –1 involution of the Leech lattice, there is an involution h of VL, and an irreducible h-twisted VLmodule, to get the Moonshine Module, one takes the fixed point subspace of h in the direct sum of VL and its twisted module. This was provided by Frenkel–Lepowsky–Meurmans construction and analysis of the Moonshine Module, a Lie algebra m, called the monster Lie algebra, is constructed from V using a quantization functor. It is a generalized Kac–Moody Lie algebra with an action by automorphisms. Using the Goddard–Thorn no-ghost theorem from string theory, the root multiplicities are found to be coefficients of J, one uses the Koike–Norton–Zagier infinite product identity to construct a generalized Kac–Moody Lie algebra by generators and relations. The identity is proved using the fact that Hecke operators applied to J yield polynomials in J, by comparing root multiplicities, one finds that the two Lie algebras are isomorphic, and in particular, the Weyl denominator formula for m is precisely the Koike–Norton–Zagier identity. Using Lie algebra homology and Adams operations, a twisted denominator identity is given for each element and these identities are related to the McKay–Thompson series Tg in much the same way that the Koike–Norton–Zagier identity is related to J. These relations are strong enough that one needs to check that the first seven terms agree with the functions given by Conway. The lowest terms are given by the decomposition of the seven lowest degree homogeneous spaces given in the first step. Borcherds was later quoted as saying I was over the moon when I proved the moonshine conjecture, I dont actually know, as I have not tested this theory of mine. More recent work has simplified and clarified the last steps of the proof, Conway and Norton suggested in their 1979 paper that perhaps moonshine is not limited to the monster, but that similar phenomena may be found for other groups. In 1987, Norton combined Queens results with his own computations to formulate the Generalized Moonshine conjecture, each f is either a constant function, or a Hauptmodul
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Theory of everything
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Finding a ToE is one of the major unsolved problems in physics. Over the past few centuries, two theoretical frameworks have been developed that, as a whole, most closely resemble a ToE and these two theories upon which all modern physics rests are general relativity and quantum field theory. GR is a framework that only focuses on gravity for understanding the universe in regions of both large-scale and high-mass, stars, galaxies, clusters of galaxies, etc. QFT successfully implemented the Standard Model and unified the interactions between the three forces, weak, strong, and electromagnetic force. Through years of research, physicists have experimentally confirmed with tremendous accuracy virtually every prediction made by two theories when in their appropriate domains of applicability. In accordance with their findings, scientists learned that GR and QFT. Since the usual domains of applicability of GR and QFT are so different, in pursuit of this goal, quantum gravity has become an area of active research. Eventually a single explanatory framework, called string theory, has emerged that intends to be the theory of the universe. String theory posits that at the beginning of the universe, the four forces were once a single fundamental force. According to string theory, every particle in the universe, at its most microscopic level, string theory further claims that it is through these specific oscillatory patterns of strings that a particle of unique mass and force charge is created. Initially, the theory of everything was used with an ironic connotation to refer to various overgeneralized theories. For example, a grandfather of Ijon Tichy — a character from a cycle of Stanisław Lems science fiction stories of the 1960s — was known to work on the General Theory of Everything. Physicist John Ellis claims to have introduced the term into the literature in an article in Nature in 1986. Over time, the term stuck in popularizations of theoretical physics research, in ancient Greece, pre-Socratic philosophers speculated that the apparent diversity of observed phenomena was due to a single type of interaction, namely the motions and collisions of atoms. The concept of atom, introduced by Democritus, was a philosophical attempt to unify all phenomena observed in nature. Archimedes was possibly the first scientist known to have described nature with axioms and he thus tried to describe everything starting from a few axioms. Any theory of everything is similarly expected to be based on axioms, in the late 17th century, Isaac Newtons description of the long-distance force of gravity implied that not all forces in nature result from things coming into contact. Laplace thus envisaged a combination of gravitation and mechanics as a theory of everything, modern quantum mechanics implies that uncertainty is inescapable, and thus that Laplaces vision has to be amended, a theory of everything must include gravitation and quantum mechanics
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Quantum gravity
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Quantum gravity is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics, and where quantum effects cannot be ignored. The current understanding of gravity is based on Albert Einsteins general theory of relativity, the necessity of a quantum mechanical description of gravity is sometimes said to follow from the fact that one cannot consistently couple a classical system to a quantum one. This is false as is shown, for example, by Walds explicit construction of a consistent semiclassical theory, the problem is that the theory one gets in this way is not renormalizable and therefore cannot be used to make meaningful physical predictions. As a result, theorists have taken up more radical approaches to the problem of quantum gravity, a theory of quantum gravity that is also a grand unification of all known interactions is sometimes referred to as The Theory of Everything. As a result, quantum gravity is a mainly theoretical enterprise, much of the difficulty in meshing these theories at all energy scales comes from the different assumptions that these theories make on how the universe works. Quantum field theory, if conceived of as a theory of particles, General relativity models gravity as a curvature within space-time that changes as a gravitational mass moves. Historically, the most obvious way of combining the two ran quickly into what is known as the renormalization problem, another possibility is to focus on fields rather than on particles, which are just one way of characterizing certain fields in very special spacetimes. This solves worries about consistency, but does not appear to lead to a version of full general theory of relativity. Quantum gravity can be treated as a field theory. Effective quantum field theories come with some high-energy cutoff, beyond which we do not expect that the theory provides a description of nature. The infinities then become large but finite quantities depending on this finite cutoff scale and this same logic works just as well for the highly successful theory of low-energy pions as for quantum gravity. Indeed, the first quantum-mechanical corrections to graviton-scattering and Newtons law of gravitation have been explicitly computed. In fact, gravity is in ways a much better quantum field theory than the Standard Model. Specifically, the problem of combining quantum mechanics and gravity becomes an issue only at high energies. This problem must be put in the context, however. While there is no proof of the existence of gravitons. The predicted find would result in the classification of the graviton as a force similar to the photon of the electromagnetic field. Many of the notions of a unified theory of physics since the 1970s assume, and to some degree depend upon
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Supersymmetry
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Each particle from one group is associated with a particle from the other, known as its superpartner, the spin of which differs by a half-integer. In a theory with perfectly unbroken supersymmetry, each pair of superpartners would share the same mass, for example, there would be a selectron, a bosonic version of the electron with the same mass as the electron, that would be easy to find in a laboratory. Thus, since no superpartners have been observed, if supersymmetry exists it must be a broken symmetry so that superpartners may differ in mass. Spontaneously-broken supersymmetry could solve many problems in particle physics including the hierarchy problem. The simplest realization of spontaneously-broken supersymmetry, the so-called Minimal Supersymmetric Standard Model, is one of the best studied candidates for physics beyond the Standard Model, there is only indirect evidence and motivation for the existence of supersymmetry. Direct confirmation would entail production of superpartners in collider experiments, such as the Large Hadron Collider, the first run of the LHC found no evidence for supersymmetry, and thus set limits on superpartner masses in supersymmetric theories. While some remain enthusiastic about supersymmetry, this first run at the LHC led some physicists to explore other ideas, the LHC resumed its search for supersymmetry and other new physics in its second run. There are numerous phenomenological motivations for supersymmetry close to the electroweak scale, supersymmetry close to the electroweak scale ameliorates the hierarchy problem that afflicts the Standard Model. In the Standard Model, the electroweak scale receives enormous Planck-scale quantum corrections, the observed hierarchy between the electroweak scale and the Planck scale must be achieved with extraordinary fine tuning. In a supersymmetric theory, on the hand, Planck-scale quantum corrections cancel between partners and superpartners. The hierarchy between the scale and the Planck scale is achieved in a natural manner, without miraculous fine-tuning. The idea that the symmetry groups unify at high-energy is called Grand unification theory. In the Standard Model, however, the weak, strong, in a supersymmetry theory, the running of the gauge couplings are modified, and precise high-energy unification of the gauge couplings is achieved. The modified running also provides a mechanism for radiative electroweak symmetry breaking. TeV-scale supersymmetry typically provides a dark matter particle at a mass scale consistent with thermal relic abundance calculations. Supersymmetry is also motivated by solutions to several problems, for generally providing many desirable mathematical properties. Supersymmetric quantum field theory is much easier to analyze, as many more problems become exactly solvable. When supersymmetry is imposed as a symmetry, Einsteins theory of general relativity is included automatically
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Supergravity
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In theoretical physics, supergravity is a field theory that combines the principles of supersymmetry and general relativity. Together, these imply that, in supergravity, the supersymmetry is a local symmetry, since the generators of supersymmetry are convoluted with the Poincaré group to form a super-Poincaré algebra, it can be seen that supergravity follows naturally from local supersymmetry. Like any field theory of gravity, a supergravity theory contains a field whose quantum is the graviton. Supersymmetry requires the graviton field to have a superpartner and this field has spin 3/2 and its quantum is the gravitino. The number of fields is equal to the number of supersymmetries. The first theory of local supersymmetry was proposed in 1975 by Dick Arnowitt, Supergravity theories with N>1 are usually referred to as extended supergravity. Some supergravity theories were shown to be related to certain higher-dimensional supergravity theories via dimensional reduction, in these classes of models collectively now known as minimal supergravity Grand Unification Theories, gravity mediates the breaking of SUSY through the existence of a hidden sector. MSUGRA naturally generates the Soft SUSY breaking terms which are a consequence of the Super Higgs effect, radiative breaking of electroweak symmetry through Renormalization Group Equations follows as an immediate consequence. One of these supergravities, the 11-dimensional theory, generated considerable excitement as the first potential candidate for the theory of everything and these problems are avoided in 12 dimensions if two of these dimensions are timelike, as has been often emphasized by Itzhak Bars. Today many techniques exist to embed the model gauge group in supergravity in any number of dimensions. For example, in the mid and late 1980s, the gauge symmetry in type I. In type II string theory they could also be obtained by compactifying on certain Calabi–Yau manifolds, today one may also use D-branes to engineer gauge symmetries. In 1978, Eugène Cremmer, Bernard Julia and Joël Scherk found the action for an 11-dimensional supergravity theory. This remains today the only known classical 11-dimensional theory with local supersymmetry, other 11-dimensional theories are known that are quantum-mechanically inequivalent to the CJS theory, but classically equivalent. For example, in the mid 1980s Bernard de Wit and Hermann Nicolai found an alternate theory in D=11 Supergravity with Local SU Invariance. In 1980, Peter Freund and M. A. Rubin showed that compactification from 11 dimensions preserving all the SUSY generators could occur in two ways, leaving only 4 or 7 macroscopic dimensions, unfortunately, the noncompact dimensions have to form an anti-de Sitter space. Many of the details of the theory were fleshed out by Peter van Nieuwenhuizen, Sergio Ferrara, the initial excitement over 11-dimensional supergravity soon waned, as various failings were discovered, and attempts to repair the model failed as well. Problems included, The compact manifolds which were known at the time and which contained the standard model were not compatible with supersymmetry, and could not hold quarks or leptons
21.
Twistor string theory
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Twistor string theory is an equivalence between N =4 supersymmetric Yang–Mills theory and the perturbative topological B model string theory in twistor space. It was initially proposed by Edward Witten in 2003, twistor theory was introduced by Roger Penrose from the 1960s as a new approach to the unification of quantum theory with gravity. Twistor space is a complex projective space in which physical quantities appear as certain structural deformations. Spacetime and the physical fields emerge as consequences of this description. But twistor space is chiral with left- and right-handed objects treated differently, for example, the graviton for gravity and the gluon for the strong force are both right-handed. During this period, Edward Witten was a developer of string theory. Witten showed that they have a simple structure in twistor space. This has allowed better understanding of experimental observations in particle colliders and deep insights into the natures of different quantum field theories. These insights have in turn led to new insights in pure mathematics, such topics include Grassmannian residue formulae, the amplituhedron and holomorphic linking
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Holographic principle
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First proposed by Gerard t Hooft, it was given a precise string-theory interpretation by Leonard Susskind who combined his ideas with previous ones of t Hooft and Charles Thorn. As pointed out by Raphael Bousso, Thorn observed in 1978 that string theory admits a lower-dimensional description in which gravity emerges from it in what would now be called a holographic way. Cosmological holography has not been made mathematically precise, partly because the horizon has a non-zero area. The holographic principle was inspired by black hole thermodynamics, which conjectures that the entropy in any region scales with the radius squared. In the case of a hole, the insight was that the informational content of all the objects that have fallen into the hole might be entirely contained in surface fluctuations of the event horizon. The holographic principle resolves the black hole information paradox within the framework of string theory, however, there exist classical solutions to the Einstein equations that allow values of the entropy larger than those allowed by an area law, hence in principle larger than those of a black hole. These are the so-called Wheelers bags of gold, the existence of such solutions conflicts with the holographic interpretation, and their effects in a quantum theory of gravity including the holographic principle are not yet fully understood. An object with relatively high entropy is microscopically random, like a hot gas, a known configuration of classical fields has zero entropy, there is nothing random about electric and magnetic fields, or gravitational waves. Since black holes are exact solutions of Einsteins equations, they were not to have any entropy either. But Jacob Bekenstein noted that this leads to a violation of the law of thermodynamics. If one throws a hot gas with entropy into a hole, once it crosses the event horizon. The random properties of the gas would no longer be seen once the black hole had absorbed the gas and settled down. One way of salvaging the second law is if black holes are in random objects with an entropy that increases by an amount greater than the entropy of the consumed gas. Bekenstein assumed that black holes are maximum entropy objects—that they have more entropy than anything else in the same volume, in a sphere of radius R, the entropy in a relativistic gas increases as the energy increases. The only known limit is gravitational, when there is too much energy the gas collapses into a black hole, Bekenstein used this to put an upper bound on the entropy in a region of space, and the bound was proportional to the area of the region. He concluded that the black hole entropy is proportional to the area of the event horizon. Stephen Hawking had shown earlier that the horizon area of a collection of black holes always increases with time. The horizon is a boundary defined by light-like geodesics, it is those light rays that are just barely unable to escape, if neighboring geodesics start moving toward each other they eventually collide, at which point their extension is inside the black hole
23.
Nima Arkani-Hamed
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Nima Arkani-Hamed is an American-Canadian of Iranian descent, who is a theoretical physicist with interests in high-energy physics, string theory and cosmology. Arkani-Hamed is now on the faculty at the Institute for Advanced Study in Princeton, New Jersey and he was formerly a professor at Harvard University and the University of California, Berkeley. Arkani-Hameds parents, Jafargholi Jafar Arkani-Hamed and Hamideh Alasti are both physicists from Iran and his father, a native of Tabriz, was chairman of the physics department at Sharif University of Technology in Tehran, and later taught earth and planetary sciences at McGill University in Montreal. Arkani-Hamed immigrated to Canada as a child with his family, the majority of his graduate work was on studies of supersymmetry and flavor physics. His Ph. D dissertation was titled Supersymmetry and Hierarchies and he completed his Ph. D in 1997 and went to SLAC at Stanford University for post-doctoral studies. During this time he worked with Savas Dimopoulos and developed the paradigm of large extra dimensions, in 1999 he joined the faculty of the University of California, Berkeley physics department. He took a leave of absence from Berkeley to visit Harvard University beginning January 2001, shortly after arriving at Harvard he worked with Howard Georgi and Andrew Cohen on the idea of emergent extra dimensions, dubbed dimensional deconstruction. These ideas eventually led to the development of little Higgs theories and he officially joined Harvards faculty in the fall of 2002. Arkani-Hamed has appeared on television programs and newspapers talking about space, time and dimensions. In 2003 he won the Gribov Medal of the European Physical Society and he appeared in the 2013 documentary film Particle Fever. He participated in the Stock Exchange of Visions project in 2007, in 2008, he won the Raymond and Beverly Sackler Prize given at Tel Aviv University to young scientists who have made outstanding and fundamental contributions in Physical Science. Arkani-Hamed was elected a Fellow of the American Academy of Arts, in 2010, he gave the Messenger lectures at Cornell University. Nima Arkani-Hamed was a professor at Harvard University from 2002–2008, and is now at the Institute for Advanced Study, Arkani-Hamed was selected for being a member of The Selection Committee for the 2015 Breakthrough Prize in Fundamental Physics. In July 2012, he was an awardee of the Fundamental Physics Prize. He has previously won the Sackler Prize from Tel Aviv University in 2008, the Gribov Medal from the European Physical Society in 2003, and he was awarded the Packard and Sloan Fellowship in 2000. The paradigm of large dimensions, N. Arkani-Hamed, S. Dimopoulos. The Hierarchy Problem and New Dimensions at a Millimeter, I Antoniadis, N. Arkani-Hamed, S. Dimopoulos, G. Dvali. New Dimensions at a Millimeter to a Fermi and Superstrings at a TeV, N. Arkani-Hamed, S. Dimopoulos, G. Dvali
24.
Robbert Dijkgraaf
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Robertus Henricus Robbert Dijkgraaf is a Dutch mathematical physicist and string theorist. He is tenured professor at the University of Amsterdam, and director, robertus Henricus Dijkgraaf was born on 24 January 1960 in Ridderkerk, Netherlands. He lives in Princeton, New Jersey, Dijkgraaf is married to the author Pia de Jong and has three children. Dijkgraaf went to Erasmiaans Gymnasium in Rotterdam, Netherlands and he started his education in physics at Utrecht University in 1978. After completing his Bachelors degree equivalent in 1982 he briefly turned away from physics to pursue painting at the Gerrit Rietveld Academie, in 1984, he returned to Utrecht University, to start on his masters degree in theoretical physics. After obtaining his MSc degree, he continued working towards his PhD under supervision of Nobel laureate Gerard t Hooft and he studied together with the twins Erik and Herman Verlinde. The original arrangement was only one of the trio would work on string theory. Dijkgraaf obtained his doctorate in 1989 cum laude and his thesis was titled A Geometrical Approach to Two Dimensional Conformal Field Theory. Subsequently, Dijkgraaf held positions at Princeton University and the Institute for Advanced Study, in 1992, he was appointed professor at the University of Amsterdam, where he held the chair of mathematical physics until 2004, when he was appointed distinguished professor at the same university. He regularly appears on Dutch television and has a column in the Dutch newspaper NRC Handelsblad, from 2008 to 2012 he was president of the Royal Netherlands Academy of Arts and Sciences. He was elected as one of the two co-chairs of the InterAcademy Council for the period 2009-2013, starting 1 July 2012 Dijkgraaf became the director of the Institute for Advanced Study in Princeton. On that date he stepped down from his position as president of the Royal Netherlands Academy of Arts, Robbert Dijkgraaf is a member of the CuriosityStream Advisory Board. In 2003, Dijkgraaf was awarded the Spinoza Prize, in doing so he became the first recipient of the award whose advisor also was a recipient. He used part of his Spinoza Prize grant to set up a website targeted at children and promoting science, Dijkgraaf is a member of the Royal Netherlands Academy of Arts and Sciences since 2003 and the Royal Holland Society of Sciences and Humanities. On 5 June 2012 he was made a Knight of the Order of the Netherlands Lion, in 2012 he became a fellow of the American Mathematical Society. Dijkgraafs research focuses on string theory and the interface of mathematics and physics in general and he is best known for his work on topological string theory and matrix models, and his name has been given to the Dijkgraaf-Witten invariants and the Witten-Dijkgraaf-Verlinde-Verlinde formula. Blikwisselingen Het nut van nutteloos onderzoek Robbert Dijkgraaf, official website Robbert Dijkgraaf, profile at the IAS website Quantum Questions Inspire New Math, Quanta Magazine, March 30,2017
25.
Michael Duff (physicist)
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Duff completed his Bachelor of Science in Physics Queen Mary College, London in 1969. He then went on to his Doctor of Philosophy in theoretical physics in 1972 at Imperial College London supervised by the Nobel Laureate Abdus Salam. He did postdoctoral fellowships at the International Centre for Theoretical Physics, University of Oxford, Kings College London, Queen Mary College London, after his postdoctoral fellowships, he returned to Imperial College in 1979 on a Science Research Council Advanced Fellowship and joined the faculty there in 1980. He took leave of absence to visit the Theory Division in CERN, first in 1982 and he took up his professorship at Texas A&M University in 1988 and was appointed Distinguished Professor in 1992. In 1999 he moved to the University of Michigan, where he was Oskar Klein Professor of Physics, in 2001, he was elected first Director of the Michigan Center for Theoretical Physics and was re-elected in 2004. He returned again to Imperial College, London and became Professor of Physics and he was appointed Abdus Salam Professor of Theoretical Physics in 2006. His interests lie in unified theories of the particles, quantum gravity, supergravity, Kaluza–Klein theory, superstrings, supermembranes. He is the author of The World in Eleven Dimensions, Supergravity, Supermembranes and M-theory, Imperial College faculty page for Duff Duffs web site Duff, M. J. Recent applications of the Weyl Anomaly, prof. Michael Duff presented and published his paper in National Center for Physics in Islamabad, Pakistan. Scientific publications of Michael Duff on INSPIRE-HEP
26.
Willy Fischler
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Willy Fischler is a theoretical physicist. He is the Jane and Roland Blumberg Centennial Professor of Physics at the University of Texas at Austin and his contributions to physics include, Early computation of the force between heavy quarks. The invisible axion, as a solution to the strong CP problem, the cosmological effects of the invisible axion and its role as a candidate for dark matter. Pioneering work on the use of supersymmetry to solve outstanding problems in the model of particle physics. The first formulation of what became known as the problem in cosmology”. The Fischler-Susskind mechanism in string theory, the original formulation of the holographic entropy bound in the context of cosmology. The discovery of M theory, or BFSS Matrix Theory, M theory is an example of a gauge/gravity duality. He is a Licensed Paramedic with Marble Falls Area EMS and was a volunteer EMT with the Westlake Fire Department
27.
Sylvester James Gates
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Sylvester James Gates Jr. known as S. James Gates Jr. or Jim Gates, is an American theoretical physicist, known for work on supersymmetry, supergravity, and superstring theory. Gates received BS and PhD degrees from the Massachusetts Institute of Technology and his doctoral thesis was the first at MIT on supersymmetry. With M. T. Grisaru, M. Rocek and W. Siegel, Gates coauthored Superspace, or One thousand and one lessons in supersymmetry and he is on the board of trustees of Society for Science & the Public. Gates was a Martin Luther King Jr, visiting Scholar at MIT and was a Residential Scholar at MITs Simmons Hall. He is pursuing ongoing research into string theory, supersymmetry, and his research focuses on Adinkra symbols as representations of supersymmetric algebras. On February 1,2013, Gates was a recipient of the National Medal of Science, Gates was elected to the National Academy of Sciences in 2013. On November 5,2016, Gates spoke at the 2016 Quadrennial Physics Congress, recently Gates has been featured in a TurboTax commercial and has been featured extensively on NOVA PBS programs on physics, notably The Elegant Universe. During the 2008 World Science Festival, Gates narrated a ballet The Elegant Universe, Gates Appeared on the 2011 Isaac Asimov Memorial Debate, The Theory of Everything, hosted by Neil DeGrasse Tyson. Gates also appeared in the BBC Horizon documentary The Hunt for Higgs in 2012, Gates recently appeared in another NOVA documentary Big Bang Machine in 2015. Superspace or 1001 Lessons in Supersymmetry, Benjamin-Cummings Publishing Company, Reading, larte della fisica superspace, Stringhe, superstringhe, teoria unificata dei campi,2006, Di Renzo Editore, ISBN 88-8323-155-4. Appearances on C-SPAN Sylvester James Gates at the Internet Movie Database
28.
Brian Greene
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Brian Randolph Greene is an American theoretical physicist and string theorist. He has been a professor at Columbia University since 1996 and chairman of the World Science Festival since co-founding it in 2008, Greene has worked on mirror symmetry, relating two different Calabi–Yau manifolds. He also described the transition, a mild form of topology change. He also appeared on The Big Bang Theory episode The Herb Garden Germination, as well as the films Frequency and he is currently a member of the Board of Sponsors of the Bulletin of the Atomic Scientists. Greene was born in New York City and his father, Alan Greene, was a one-time vaudeville performer and high school dropout who later worked as a voice coach and composer. He stated in an interview with Lawrence Krauss that he is of Jewish heritage, after attending Stuyvesant High School, Greene entered Harvard in 1980 to concentrate on physics. After completing his bachelors degree, Greene earned his doctorate from Oxford University as a Rhodes Scholar, while at Oxford, Greene also studied piano with the concert pianist Jack Gibbons. Greene joined the faculty of Cornell University in 1990, and was appointed to a full professorship in 1995. The following year, he joined the staff of Columbia University as a full professor and he is also one of the FQXi large grant awardees, his project title being Arrow of Time in the Quantum Universe. His co-investigators are David Albert and Maulik Parikh, greenes area of research is string theory, a candidate for a theory of quantum gravity. String theory attempts to explain the different particle species of the model of particle physics as different aspects of a single type of one-dimensional. The theory has several explanations to offer for why we do not perceive these extra dimensions, in the field, Greene is best known for his contribution to the understanding of the different shapes the curled-up dimensions of string theory can take. Greene has worked on a class of symmetry relating two different Calabi–Yau manifolds, known as mirror symmetry. He is also known for his research on the flop transition and he is currently the Chairman of the Board. The World Science Festival’s signature event is a festival in New York City. The first six Festivals have drawn close to a million visitors, Greene is well known to a wider audience for his work on popularizing theoretical physics, in particular string theory and the search for a unified theory of physics. His first book, The Elegant Universe, Superstrings, Hidden Dimensions, and it was a finalist for the Pulitzer Prize in nonfiction, and winner of The Aventis Prizes for Science Books in 2000. The Elegant Universe was later made into a PBS television special of the name, hosted and narrated by Greene
29.
David Gross
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David Jonathan Gross is an American theoretical physicist and string theorist. Along with Frank Wilczek and David Politzer, he was awarded the 2004 Nobel Prize in Physics for their discovery of asymptotic freedom. He is the director and current holder of the Frederick W. Gluck Chair in Theoretical Physics at the Kavli Institute for Theoretical Physics of the University of California. He is also a faculty member in the UC Santa Barbara Physics Department and is affiliated with the Institute for Quantum Studies at Chapman University in California. He is the Foreign Member of Chinese Academy of Sciences, Gross was born to a Jewish family in Washington, D. C. in February 19,1941. His parents were Nora and Bertram Myron Gross, Gross received his bachelors degree and masters degree from the Hebrew University of Jerusalem, Israel, in 1962. He received his Ph. D. in physics from the University of California, Berkeley and he was a Junior Fellow at Harvard University and a Professor at Princeton University until 1997. He was the recipient of a MacArthur Foundation Fellowship in 1987, the Dirac Medal in 1988, asymptotic freedom, independently discovered by Politzer, was important for the development of quantum chromodynamics. Gross, with Jeffrey A. Harvey, Emil Martinec, the four were to be whimsically nicknamed the Princeton String Quartet. In 2003, Gross was one of 22 Nobel Laureates who signed the Humanist Manifesto and they have two children, Ariela Gross, who is an historian and professor of law at the University of Southern California and the mother of his grandchildren, Raphaela and Sophia. Elisheva Gross, who received a Doctor in psychology at the University of California at Los Angeles and his second wife is Jacquelyn Savani. He has a stepdaughter, Miranda Savani, in Santa Barbara, California
30.
Michio Kaku
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Michio Kaku is an American theoretical physicist, futurist, and popularizer of science. Kaku is a professor of physics at the City College of New York. He has written books about physics and related topics, has made frequent appearances on radio, television, and film. He has written three New York Times best sellers, Physics of the Impossible, Physics of the Future, Kaku has hosted several TV specials for the BBC, the Discovery Channel, the History Channel, and the Science Channel. Kaku was born in San Jose, California, to Japanese American parents and his father, born in California and educated in both Japan and the United States, was fluent in Japanese and English. Both his parents were interned in the Tule Lake War Relocation Center during World War II, where they met, while attending Cubberley High School in Palo Alto, Kaku assembled a particle accelerator in his parents garage for a science fair project. His admitted goal was to generate a beam of gamma rays powerful enough to create antimatter, at the National Science Fair in Albuquerque, New Mexico, he attracted the attention of physicist Edward Teller, who took Kaku as a protégé, awarding him the Hertz Engineering Scholarship. Kaku graduated summa cum laude from Harvard University in 1968 and was first in his physics class. He attended the Berkeley Radiation Laboratory at the University of California, Berkeley, and received a Ph. D. in 1972, Kaku was drafted into the United States Army during the Vietnam War. He completed his training at Fort Benning, Georgia, and advanced infantry training at Fort Lewis. However, the Vietnam War ended before he was deployed as an infantryman, as part of the research program in 1975 and 1977 at the department of physics at The City College of The City University of New York, Kaku worked on research on quantum mechanics. He was a Visitor and Member at the Institute for Advanced Study in Princeton and he currently holds the Henry Semat Chair and Professorship in theoretical physics at the City College of New York. Kaku had a role in breaking the SSFL story in 1979, the Santa Susana facility run by RocketDyne was responsible for an experimental sodium reactor which had an accident in Simi Valley in the 50s. Kaku was a student involved in breaking the story of the leak of radiation, Kaku has had more than 70 articles published in physics journals such as Physical Review, covering topics such as superstring theory, supergravity, supersymmetry, and hadronic physics. In 1974, Kaku and Prof. Keiji Kikkawa of Osaka University co-authored the first papers describing string theory in a field form, Kaku is the author of several textbooks on string theory and quantum field theory. Kaku is most widely known as a popularizer of science and physics outreach specialist and he has written books and appeared on many television programs as well as film. He also hosts a radio program. Parallel Worlds was a finalist for the Samuel Johnson Prize for nonfiction in the UK, Kaku is the host of the weekly one-hour radio program Exploration, produced by the Pacifica Foundations WBAI in New York
31.
Maxim Kontsevich
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Maxim Lvovich Kontsevich is a Russian and French mathematician. He is a professor at the Institut des Hautes Études Scientifiques and he was born into the family of Lev Rafailovich Kontsevich, Soviet orientalist and author of the Kontsevich system. In 1992 he received his Ph. D. at the University of Bonn under Don Bernard Zagier and his thesis outlines a proof of a conjecture by Edward Witten that two quantum gravitational models are equivalent. His work concentrates on geometric aspects of physics, most notably on knot theory, quantization. One of his results is a formal deformation quantization that holds for any Poisson manifold and he also introduced knot invariants defined by complicated integrals analogous to Feynman integrals. In topological field theory, he introduced the space of stable maps. In 1998, he won the Fields Medal for his contributions to four problems of Geometry, in July 2012, he was an inaugural awardee of the Fundamental Physics Prize, the creation of physicist and internet entrepreneur, Yuri Milner. Taubes, Clifford Henry The work of Maxim Kontsevich, in Proceedings of the International Congress of Mathematicians, Vol. I. OConnor, John J. Robertson, Edmund F, Maxim Kontsevich, MacTutor History of Mathematics archive, University of St Andrews. Maxim Kontsevich at the Mathematics Genealogy Project AMS Profile of Maxim Kontsevich Official Homepage of Maxim Kontsevich Stankova, videos of Maxim Konzewitsch in the AV-Portal of the German National Library of Science and Technology
32.
Andrei Linde
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Andrei Dmitriyevich Linde is a Russian-American theoretical physicist and the Harald Trap Friis Professor of Physics at Stanford University. Linde is one of the authors of the inflationary universe theory, as well as the theory of eternal inflation. He received his Bachelor of Science degree from Moscow State University, in 1975, Linde was awarded a Ph. D. from the Lebedev Physical Institute in Moscow. He worked at CERN since 1989 and moved to the USA in 1990 where he became Professor of Physics at Stanford University. Among the various awards hes received for his work on inflation, in 2002 he was awarded the Dirac Medal, along with Alan Guth of MIT, in 2004 he received, along with Alan Guth, the Gruber Prize in Cosmology for the development of inflationary cosmology. In 2012 he, along with Alan Guth, was an awardee of the Fundamental Physics Prize. In 2014 he received the Kavli Prize in Astrophysics “for pioneering the theory of inflation, together with Alan Guth. During 1972 to 1976, David Kirzhnits and Andrei Linde developed a theory of phase transitions. According to this theory, there was not much difference between weak, strong and electromagnetic interactions in the early universe. These interactions became different from each other only gradually, after the phase transitions while the Universe expanded and cooled down. In 1974, Linde found that the density of scalar fields that break the symmetry between different interactions can play the role of the vacuum energy density in the Einstein equations. Between 1976 and 1978, Linde demonstrated that the release of energy during the cosmological phase transitions may be sufficient to heat up the universe. These observations became the main ingredients of the first version of the inflationary universe theory proposed by Alan Guth in 1980 and this theory, now called the Old inflation theory, was based on the assumption that the universe was initially hot. It then experienced the cosmological phase transitions and was stuck in a supercooled metastable vacuum state. The universe then expanded exponentially – inflated – until the false vacuum decayed and this idea attracted much attention because it could provide a unique solution to many difficult problems of the standard Big Bang theory. In particular, it could explain why the universe is so large, however, as Guth immediately realized, this scenario did not quite work as intended, the decay of the false vacuum would make the universe extremely inhomogeneous. In 1981, Linde developed another version of inflationary theory which he called New inflation and he demonstrated that the exponentially rapid expansion of the universe could occur not only in the false vacuum but also during a slow transition away from the false vacuum. This theory resolved the problems of the model proposed by Guth while preserving most of its attractive features