1.
String theory
–
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
–
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
–
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
–
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
–
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
–
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
–
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