[35], In the first superstring revolution in 1984, many physicists turned to string theory as a unified theory of particle physics and quantum gravity. Physicists studying string theory have discovered a number of these dualities between different versions of string theory, and this has led to the conjecture that all consistent versions of string theory are subsumed in a single framework known as M-theory. This understanding changed in 1995 when Edward Witten suggested that the five theories were just special limiting cases of an eleven-dimensional theory called M-theory. This property is usually referred to as unitarity of time evolution. String theory describes how these strings propagate through space and interact with each other. [2] 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. At the same time, quantum chromodynamics was recognized as the correct theory of hadrons, shifting the attention of physicists and apparently leaving the bootstrap program in the dustbin of history. [66][67], One approach to formulating string theory and studying its properties is provided by the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. Because string theory potentially provides a unified description of gravity and particle physics, it is a candidate for a theory of everything, a self-contained mathematical model that describes all fundamental forces and forms of matter. However, as one approaches the hose, one discovers that it contains a second dimension, its circumference. So he hypothesized that string theory on a near-horizon extreme-charged black-hole geometry, an anti-de Sitter space times a sphere with flux, is equally well described by the low-energy limiting gauge theory, the N = 4 supersymmetric Yang–Mills theory. For example, Montonen–Olive duality is example of an S-duality relationship between quantum field theories. The resulting geometric object is three-dimensional anti-de Sitter space. Thus string theory is a theory of quantum gravity. That's what gets most people into it. String Theory, which is described as follows: String theory was originally developed during the late 1960s and early 1970s as a never completely successful theory of hadrons, the subatomic particles like the proton and neutron that feel the strong interaction. One of the problems was that the laws of physics appear to distinguish between clockwise and counterclockwise, a phenomenon known as chirality. The calculation showed that the ratio of two quantities associated with the quark–gluon plasma, the shear viscosity and volume density of entropy, should be approximately equal to a certain universal constant. In a paper from 1996, Hořava and Witten wrote "As it has been proposed that the eleven-dimensional theory is a supermembrane theory but there are some reasons to doubt that interpretation, we will non-committally call it the M-theory, leaving to the future the relation of M to membranes. in 2003. [114] Miranda Cheng, John Duncan, and Jeffrey A. Harvey proposed a generalization of this moonshine phenomenon called umbral moonshine,[115] and their conjecture was proved mathematically by Duncan, Michael Griffin, and Ken Ono. And low energy means energies much less than some … These are defined as black holes with the lowest possible mass compatible with a given charge. In this particular example, the group is known as the dihedral group of order 6 because it has six elements. One of the vibrational states of a string corresponds to the graviton, a quantum mechanical particle that carries the gravitational force. [35] Another feature of string theory that many physicists were drawn to in the 1980s and 1990s was its high degree of uniqueness. In physics, a matrix model is a particular kind of physical theory whose mathematical formulation involves the notion of a matrix in an important way. [78], In addition to its applications to theoretical problems in quantum gravity, the AdS/CFT correspondence has been applied to a variety of problems in quantum field theory. If one picks among this large set just those states whose properties agree with present experimental observations, it is likely there still will be such a large number of these that one can get just about whatever value one wants for the results of any new observation. [43] In the months following Witten's announcement, hundreds of new papers appeared on the Internet confirming different parts of his proposal. Jones, Andrew Zimmerman. These strings, the size of the Planck length (10-35 m), vibrate at specific resonant frequencies. [28], Regardless of whether Calabi–Yau compactifications of string theory provide a correct description of nature, the existence of the mirror duality between different string theories has significant mathematical consequences. The surface of this cylinder plays an important role in 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. 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. This hypothesis, which is called the AdS/CFT correspondence, was further developed by Steven Gubser, Igor Klebanov and Alexander Polyakov,[69] and by Edward Witten,[70] and it is now well-accepted. [20], One notable feature of string theories is that these theories require extra dimensions of spacetime for their mathematical consistency. Physicists must apply perturbation theory to obtain a series of approximated solutions. Stephen Shenker showed it diverged much faster than in field theory suggesting that new non-perturbative objects were missing. [106] Although this function appears in a branch of mathematics which seems very different from the theory of finite groups, the two subjects turn out to be intimately related. String theory has proved to be an important tool for investigating the theoretical properties of black holes because it provides a framework in which theorists can study their thermodynamics. In his book The Trouble With Physics, physicist Lee Smolin of the Perimeter Institute for Theoretical Physics claims that this is the principal weakness of string theory as a theory of quantum gravity, saying that string theory has failed to incorporate this important insight from general relativity. While there has been progress toward these goals, it is not known to what extent string theory describes the real world or how much freedom the theory allows in the choice of details. For example, the atoms slow to a halt at a rate that depends on the temperature and on Planck's constant, the fundamental parameter of quantum mechanics, which does not enter into the description of the other phases. A quantum theory of gravity is needed in order to reconcile general relativity with the principles of quantum mechanics, but difficulties arise when one attempts to apply the usual prescriptions of quantum theory to the force of gravity. For example, a string has momentum as it propagates around a circle, and it can also wind around the circle one or more times. It has spin and replace Standard Model particles with symmetries. Put differently, the two theories are mathematically different descriptions of the same phenomena. This problem was solved by the nineteenth-century German mathematician Hermann Schubert, who found that there are exactly 2,875 such lines. [113], Since the 1990s, the connection between string theory and moonshine has led to further results in mathematics and physics. Following Witten's lead, between 1984 and 1986, hundreds of physicists started to work in this field, and this is sometimes called the first superstring revolution. Since the superstring revolutions of the 1980s and 1990s, string theory has become the dominant paradigm of high energy theoretical physics. String theory has contributed a number of advances to mathematical physics, which have been applied to a variety of problems in black hole physics, early universe cosmology, nuclear physics, and condensed matter physics, and it has stimulated a number of major developments in pure mathematics. The result was widely advertised by Murray Gell-Mann, leading Gabriele Veneziano to construct a scattering amplitude that had the property of Dolen–Horn–Schmid duality, later renamed world-sheet duality. [72], This construction describes a hypothetical universe with only two space dimensions and one time dimension, but it can be generalized to any number of dimensions. [71], An important feature of anti-de Sitter space is its boundary (which looks like a cylinder in the case of three-dimensional anti-de Sitter space). [121], String theorist Leonard Susskind has argued that string theory provides a natural anthropic explanation of the small value of the cosmological constant. version of string theory. The Bekenstein–Hawking entropy formula gives the expected value of the entropy of a black hole, but by the 1990s, physicists still lacked a derivation of this formula by counting microstates in a theory of quantum gravity. David Gross and Vipul Periwal discovered that string perturbation theory was divergent. Thus while quantum chromodynamics (or ‘QED’) is a part of the standard model, it is an instance of a quantum field theory, or short “a quantum field theory” and not a part of QFT. In bosonic string theory, spacetime is 26-dimensional, while in superstring theory it is 10-dimensional, and in M-theory it is 11-dimensional. In a review of Smolin's book, string theorist Joseph Polchinski writes, [Smolin] is mistaking an aspect of the mathematical language being used for one of the physics being described. While these approaches might eventually find support in observational data such as measurements of the cosmic microwave background, the application of string theory to cosmology is still in its early stages. [56] At first, Hawking's result posed a problem for theorists because it suggested that black holes destroy information. Subsequently, it was realized that the very properties that made string theory unsuitable as a theory of nuclear physics made it a promising candidate for a quantum theory of gravity. M-theory was also foreshadowed in the work of Paul Townsend at approximately the same time. A celebrated result of nineteenth-century mathematicians Arthur Cayley and George Salmon states that there are exactly 27 straight lines that lie entirely on such a surface. These states are described using the formalism of quantum field theory, but some phenomena are difficult to explain using standard field theoretic techniques. This observation is the starting point for AdS/CFT correspondence, which states that the boundary of anti-de Sitter space can be regarded as the "spacetime" for a quantum field theory. The theory of cosmic inflation preserves the successes of the Big Bang while providing a natural explanation for some of the mysterious features of the universe. The number of times the string winds around a circle is called the winding number. String theory eventually made it out of the dustbin, but for the following decade all work on the theory was completely ignored. String theory's claim that all molecules are strings of energy has drawn harsh criticism. However, mathematicians generally prefer rigorous proofs that do not require an appeal to physical intuition. The Basics of String Theory. Bosonic string theory was eventually superseded by theories called superstring theories. [112] In 1998, Borcherds was awarded the Fields medal for his work. For example, type IIA string theory is equivalent to type IIB string theory via T-duality, and the two versions of heterotic string theory are also related by T-duality. There are five independent superstring theories: M-Theory: A superstring theory, proposed in 1995, which attempts to consolidate the Type I, Type IIA, Type IIB, Type HO, and Type HE models as variants of the same fundamental physical model. A grammar G can be formally written as a 4-tuple (N, T, S, P) where − N or V N is a set of variables or non-terminal symbols. This is because the standard model fails to incorporate the force of gravity and because of problems such as the hierarchy problem and the inability to explain the structure of fermion masses or dark matter. Each of these operations is called a symmetry, and the collection of these symmetries satisfies certain technical properties making it into what mathematicians call a group. Type I string theory turns out to be equivalent by S-duality to the SO(32) heterotic string theory. [f] One of the major achievements of contemporary group theory is the classification of finite simple groups, a mathematical theorem which provides a list of all possible finite simple groups. These issues have led some in the community to criticize these approaches to physics, and to question the value of continued research on string theory unification. Chew advocated making a theory for the interactions of these trajectories that did not presume that they were composed of any fundamental particles, but would construct their interactions from self-consistency conditions on the S-matrix. In the currently accepted models of stellar evolution, black holes are thought to arise when massive stars undergo gravitational collapse, and many galaxies are thought to contain supermassive black holes at their centers. [103], Group theory is the branch of mathematics that studies the concept of symmetry. [65] In collaboration with several other authors in 2010, he showed that some results on black hole entropy could be extended to non-extremal astrophysical black holes. [92], Generalizing this problem, one can ask how many lines can be drawn on a quintic Calabi–Yau manifold, such as the one illustrated above, which is defined by a polynomial of degree five. In some cases, by modeling spacetime in a different number of dimensions, a theory becomes more mathematically tractable, and one can perform calculations and gain general insights more easily. [130], Polchinski notes that an important open problem in quantum gravity is to develop holographic descriptions of gravity which do not require the gravitational field Claud Lovelace calculated a loop amplitude, and noted that there is an inconsistency unless the dimension of the theory is 26. The string theory group believed there couldn’t be 24 dimensions. More precisely, one cannot apply the methods of perturbative quantum field theory. [48] This was the first definition of string theory that was fully non-perturbative and a concrete mathematical realization of the holographic principle. 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. Ferdinando Gliozzi, Joël Scherk, and David Olive realized in 1977 that the original Ramond and Neveu Schwarz-strings were separately inconsistent and needed to be combined. In string theory, one must typically specify a fixed reference geometry for spacetime, and all other possible geometries are described as perturbations of this fixed one. His announcement led to a flurry of research activity now known as the second superstring revolution. Leonard Susskind had incorporated the holographic principle of Gerardus 't Hooft into string theory, identifying the long highly excited string states with ordinary thermal black hole states. The latter groups are called the "sporadic" groups, and each one owes its existence to a remarkable combination of circumstances. Unlike supergravity theory, string theory was able to accommodate the chirality of the standard model, and it provided a theory of gravity consistent with quantum effects. In such models, the force-carrying bosons of particle physics arise from open strings with endpoints attached to the four-dimensional subspace, while gravity arises from closed strings propagating through the larger ambient space. [86], In the theory of inflation, the rapid initial expansion of the universe is caused by a hypothetical particle called the inflaton. It later developed into superstring theory, which posits a connection called supersymmetry between bosons and the class of particles called fermions. [77] In 2005, Hawking announced that the paradox had been settled in favor of information conservation by the AdS/CFT correspondence, and he suggested a concrete mechanism by which black holes might preserve information. Superstring theory (short for "supersymmetric string theory") incorporates bosons with another particle, fermions, as well as supersymmetry to model gravity. The flurry of activity that began at this time is sometimes called the second superstring revolution.[31]. The theory of formal languages finds its applicability extensively in the fields of Computer Science. This behavior has recently been understood by considering a dual description where properties of the fluid are described in terms of a higher dimensional black hole.[8].

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