Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modeling them as vibrations of tiny supersymmetric strings.
'Superstring theory' is a shorthand for supersymmetric string theory because unlike bosonic string theory, it is the version of string theory that accounts for both fermions and bosons and incorporates supersymmetry to model gravity.
Since the second superstring revolution, the five superstring theories are regarded as different limits of a single theory tentatively called M-theory.
The deepest problem in theoretical physics is harmonizing the theory of general relativity, which describes gravitation and applies to large-scale structures (stars, galaxies, super clusters), with quantum mechanics, which describes the other three fundamental forces acting on the atomic scale.
The development of a quantum field theory of a force invariably results in infinite possibilities. Physicists developed the technique of renormalization to eliminate these infinities; this technique works for three of the four fundamental forces—electromagnetic, strong nuclear and weak nuclear forces—but not for gravity. Development of quantum theory of gravity therefore requires different means than those used for the other forces.^{[1]}
According to the theory, the fundamental constituents of reality are strings of the Planck length (about 10^{−33} cm) that vibrate at resonant frequencies. Every string, in theory, has a unique resonance, or harmonic. Different harmonics determine different fundamental particles. The tension in a string is on the order of the Planck force (10^{44} newtons). The graviton (the proposed messenger particle of the gravitational force), for example, is predicted by the theory to be a string with wave amplitude zero.
Investigating how a string theory may include fermions in its spectrum led to the invention of supersymmetry (in the West)^{[2]} in 1971,^{[3]} a mathematical transformation between bosons and fermions. String theories that include fermionic vibrations are now known as "superstring theories".
Since its beginnings in the seventies and through the combined efforts of many different researchers, superstring theory has developed into a broad and varied subject with connections to quantum gravity, particle and condensed matter physics, cosmology, and pure mathematics.
Superstring theory is based on supersymmetry. No supersymmetric particles have been discovered and recent research at LHC and Tevatron has excluded some of the ranges.^{[4]}^{[5]}^{[6]}^{[7]} 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.^{[8]} 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.^{[9]}
Some particle physicists became disappointed^{[10]} by the lack of experimental verification of supersymmetry, and some have already discarded it; Jon Butterworth at University College London said that we had no sign of supersymmetry, even in higher energy region, excluding the superpartners of the top quark up to a few TeV. Ben Allanach at the University of Cambridge states that if we do not discover any new particles in the next trial at the LHC, then we can say it is unlikely to discover supersymmetry at CERN in the foreseeable future.^{[10]}
Our physical space is observed to have three large spatial dimensions and, along with time, is a boundless 4-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 (3D regular space + 1 time + 6D hyperspace).^{[11]} The fact that we see only 3 dimensions of space can be explained by one of two mechanisms: either the extra dimensions are compactified on a very small scale, or else our world may live on a 3-dimensional submanifold corresponding to a brane, on which all known particles besides gravity would be restricted.
If the extra dimensions are compactified, then the extra 6 dimensions must be in the form of a Calabi–Yau manifold. Within the more complete framework of M-theory, they would have to take 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 (which exchanges momentum modes for winding number and sends compact dimensions of radius R to radius 1/R),^{[12]} has led to the discovery of equivalences between different Calabi–Yau manifolds called mirror symmetry.
Superstring theory is not the first theory to propose extra spatial dimensions. It can be seen as building upon the Kaluza–Klein theory, which proposed a 4+1 dimensional (5D) 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. Thus the original Kaluza–Klein theory is a prototype for the unification of gauge and gravity interactions, at least at the classical level, however it is known to be insufficient to describe nature for a variety of reasons (missing weak and strong forces, lack of parity violation, etc.) A more complex compact geometry is needed to reproduce the known gauge forces. 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. A possible solution for this dilemma was suggested at the beginning of what is called the second superstring revolution in the 1990s, which suggests that the five string theories might be different limits of a single underlying theory, called M-theory. This remains a conjecture.^{[13]}
String theories | |||||||
---|---|---|---|---|---|---|---|
Type | Spacetime dimensions | SUSY generators | chiral | open strings | heterotic compactification | gauge group | tachyon |
Bosonic (closed) | 26 | N = 0 | no | no | no | none | yes |
Bosonic (open) | 26 | N = 0 | no | yes | no | U(1) | yes |
I | 10 | N = (1,0) | yes | yes | no | SO(32) | no |
IIA | 10 | N = (1,1) | no | no | no | U(1) | no |
IIB | 10 | N = (2,0) | yes | no | no | none | no |
HO | 10 | N = (1,0) | yes | no | yes | SO(32) | no |
HE | 10 | N = (1,0) | yes | no | yes | E_{8} × E_{8} | no |
M-theory | 11 | N = 1 | no | no | no | none | no |
The five consistent superstring theories are:
Chiral gauge theories can be inconsistent due to anomalies. This happens when certain one-loop Feynman diagrams cause a quantum mechanical breakdown of the gauge symmetry. The anomalies were canceled out via the Green–Schwarz mechanism.
Even though there are only five superstring theories, making detailed predictions for real experiments requires information about exactly what physical configuration the theory is in. This considerably complicates efforts to test string theory because there is an astronomically high number—10^{500} or more—of configurations that meet some of the basic requirements to be consistent with our world. Along with the extreme remoteness of the Planck scale, this is the other major reason it is hard to test superstring theory.
Another approach to the number of superstring theories refers to the mathematical structure called composition algebra. In the findings of abstract algebra there are just seven composition algebras over the field of real numbers. In 1990 physicists R. Foot and G.C. Joshi in Australia stated that "the seven classical superstring theories are in one-to-one correspondence to the seven composition algebras".^{[14]}
General relativity typically deals with situations involving large mass objects in fairly large regions of spacetime whereas quantum mechanics is generally reserved for scenarios at the atomic scale (small spacetime regions). The two are very rarely used together, and the most common case that combines them is in the study of black holes. Having peak density, or the maximum amount of matter possible in a space, and very small area, the two must be used in synchrony to predict conditions in such places. Yet, when used together, the equations fall apart, spitting out impossible answers, such as imaginary distances and less than one dimension.
The major problem with their congruence is that, at Planck scale (a fundamental small unit of length) lengths, general relativity predicts a smooth, flowing surface, while quantum mechanics predicts a random, warped surface, which are nowhere near compatible. Superstring theory resolves this issue, replacing the classical idea of point particles with strings. These strings have an average diameter of the Planck length, with extremely small variances, which completely ignores the quantum mechanical predictions of Planck-scale length dimensional warping. Also, these surfaces can be mapped as branes. These branes can be viewed as objects with a morphism between them. In this case, the morphism will be the state of a string that stretches between brane A and brane B.
Singularities are avoided because the observed consequences of "Big Crunches" never reach zero size. In fact, should the universe begin a "big crunch" sort of process, string theory dictates that the universe could never be smaller than the size of one string, at which point it would actually begin expanding.
D-branes are membrane-like objects in 10D string theory. They can be thought of as occurring as a result of a Kaluza–Klein compactification of 11D M-theory that contains membranes. Because compactification of a geometric theory produces extra vector fields the D-branes can be included in the action by adding an extra U(1) vector field to the string action.
In type I open string theory, the ends of open strings are always attached to D-brane surfaces. A string theory with more gauge fields such as SU(2) gauge fields would then correspond to the compactification of some higher-dimensional theory above 11 dimensions, which is not thought to be possible to date. Furthermore, the tachyons attached to the D-branes show the instability of those d-branes with respect to the annihilation. The tachyon total energy is (or reflects) the total energy of the D-branes.
For a 10 dimensional supersymmetric theory we are allowed a 32-component Majorana spinor. This can be decomposed into a pair of 16-component Majorana-Weyl (chiral) spinors. There are then various ways to construct an invariant depending on whether these two spinors have the same or opposite chiralities:
Superstring model | Invariant |
---|---|
Heterotic | |
IIA | |
IIB |
The heterotic superstrings come in two types SO(32) and E_{8}×E_{8} as indicated above and the type I superstrings include open strings.
It is conceivable that the five superstring theories are approximated to a theory in higher dimensions possibly involving membranes. Because the action for this involves quartic terms and higher so is not Gaussian, the functional integrals are very difficult to solve and so this has confounded the top theoretical physicists. Edward Witten has popularised the concept of a theory in 11 dimensions M-theory involving membranes interpolating from the known symmetries of superstring theory. It may turn out that there exist membrane models or other non-membrane models in higher dimensions—which may become acceptable when we find new unknown symmetries of nature, such as noncommutative geometry. It is thought, however, that 16 is probably the maximum since SO(16) is a maximal subgroup of E8, the largest exceptional Lie group, and also is more than large enough to contain the Standard Model. Quartic integrals of the non-functional kind are easier to solve so there is hope for the future. This is the series solution, which is always convergent when a is non-zero and negative:
In the case of membranes the series would correspond to sums of various membrane interactions that are not seen in string theory.
Investigating theories of higher dimensions often involves looking at the 10 dimensional superstring theory and interpreting some of the more obscure results in terms of compactified dimensions. For example, D-branes are seen as compactified membranes from 11D M-theory. Theories of higher dimensions such as 12D F-theory and beyond produce other effects, such as gauge terms higher than U(1). The components of the extra vector fields (A) in the D-brane actions can be thought of as extra coordinates (X) in disguise. However, the known symmetries including supersymmetry currently restrict the spinors to 32-components—which limits the number of dimensions to 11 (or 12 if you include two time dimensions.) Some commentators (e.g., John Baez et al.) have speculated that the exceptional Lie groups E_{6}, E_{7} and E_{8} having maximum orthogonal subgroups SO(10), SO(12) and SO(16) may be related to theories in 10, 12 and 16 dimensions; 10 dimensions corresponding to string theory and the 12 and 16 dimensional theories being yet undiscovered but would be theories based on 3-branes and 7-branes respectively. However, this is a minority view within the string community. Since E_{7} is in some sense F_{4} quaternified and E_{8} is F_{4} octonified, the 12 and 16 dimensional theories, if they did exist, may involve the noncommutative geometry based on the quaternions and octonions respectively. From the above discussion, it can be seen that physicists have many ideas for extending superstring theory beyond the current 10 dimensional theory, but so far all have been unsuccessful.
Since strings can have an infinite number of modes, the symmetry used to describe string theory is based on infinite dimensional Lie algebras. Some Kac–Moody algebras that have been considered as symmetries for M-theory have been E_{10} and E_{11} and their supersymmetric extensions.
Professor Asad Naqvi (Urdu:أسد نقوی), works at Goldman Sachs. Previously, he worked in theoretical physics, and superstring theory. He was an Associate Professor of Physics at the School of Science and Engineering of the Lahore University of Management Sciences (LUMS). Before joining LUMS, he was a lecturer of Physics at the University of Wales, Swansea.
Beyond Einstein (book)Beyond Einstein: The Cosmic Quest for the Theory of the Universe is a book by Michio Kaku, a theoretical physicist from the City College of New York, and Jennifer Trainer Thompson. It focuses on the development of superstring theory, which might become the unified field theory of the strong force, the weak force, electromagnetism and gravity. The book was initially published on February 1, 1987, by Bantam Books.
Brane cosmologyBrane cosmology refers to several theories in particle physics and cosmology related to string theory, superstring theory and M-theory.
Calabi–Yau manifoldIn algebraic geometry, a Calabi–Yau manifold, also known as a Calabi–Yau space, is a particular type of manifold which has properties, such as Ricci flatness, yielding applications in theoretical physics. Particularly in superstring theory, the extra dimensions of spacetime are sometimes conjectured to take the form of a 6-dimensional Calabi–Yau manifold, which led to the idea of mirror symmetry. Their name was coined by Candelas et al. (1985), after Eugenio Calabi (1954, 1957) who first conjectured that such surfaces might exist, and Shing-Tung Yau (1978) who proved the Calabi conjecture.
Calabi–Yau manifolds are complex manifolds that are generalizations of K3 surfaces in any number of complex dimensions (i.e. any even number of real dimensions). They were originally defined as compact Kähler manifolds with a vanishing first Chern class and a Ricci-flat metric, though many other similar but inequivalent definitions are sometimes used.
Glossary of string theoryThis page is a glossary of terms in string theory, including related areas such as supergravity, supersymmetry, and high energy physics.
Green–Schwarz mechanismThe Green–Schwarz mechanism (sometimes called the Green–Schwarz anomaly cancellation mechanism) is the main discovery that started the first superstring revolution in superstring theory.
Hanany–Witten transitionIn theoretical physics the Hanany–Witten transition, also called the Hanany–Witten effect, refers to any process in a superstring theory in which two p-branes cross resulting in the creation or destruction of a third p-brane. A special case of this process was first discovered by Amihay Hanany and Edward Witten in their 1996 paper Type IIB Superstrings, BPS Monopoles, And Three-Dimensional Gauge Dynamics. All other known cases of Hanany–Witten transitions are related to the original case via combinations of S-dualities and T-dualities.This effect can be expanded to string theory, 2 strings cross together resulting in the creation or destruction of a third string.
Hirosi OoguriHirosi Ooguri (spelled as Hiroshi Oguri in government documents) (大栗 博司, born 1962) is a theoretical physicist at California Institute of Technology. He is a leading theorist in high energy physics and works at the interface of elementary particle physics, string theory, and related mathematics.
Hirosi Ooguri discovers hidden geometric and algebraic structures in quantum field theory and superstring theory, and exploits them to invent new theoretical tools to investigate these theories. In particular, he developed the topological string theory to compute Feynman diagrams in superstring theory and used it to solve mysterious quantum mechanical properties of black holes. He also made fundamental contributions to conformal field theories in two dimensions, D-branes in Calabi-Yau manifolds, the AdS/CFT correspondence, and properties of supersymmetric gauge theories and their relations to superstring theory.
History of string theoryThe history of string theory spans several decades of intense research including two superstring revolutions. Through the combined efforts of many researchers, string theory has developed into a broad and varied subject with connections to quantum gravity, particle and condensed matter physics, cosmology, and pure mathematics.
Matrix string theoryIn physics, matrix string theory is a set of equations that describe superstring theory in a non-perturbative framework. Type IIA string theory can be shown to be equivalent to a maximally supersymmetric two-dimensional gauge theory, the gauge group of which is U(N) for a large value of N. This matrix string theory was first proposed by Luboš Motl in 1997 and later independently in a more complete paper by Robbert Dijkgraaf, Erik Verlinde, and Herman Verlinde. Another matrix string theory equivalent to Type IIB string theory was constructed in 1996 by Ishibashi, Kawai, Kitazawa and Tsuchiya. This version is known as the IKKT matrix model.
Picture (string theory)In superstring theory, each state may be represented in many ways, depending on how the ground state is defined. Each representation is called a picture, and is denoted by a number, such as 0 picture or −1 picture.
The difference between the ground states is according to the action of the superghosts oscillators on them, and the number of the picture (plus 1/2) reflects the highest superghost oscillator which does not annihilate the ground state.
Pierre RamondPierre Ramond (; born 31 January 1943 is distinguished professor of physics at University of Florida in Gainesville, Florida. He initiated the development of superstring theory.
Seifallah Randjbar-DaemiSeifallah Randjbar-Daemi (Persian: سیف الله رنجبر دائمی, born 1950) is an Iranian theoretical physicist. He is Assistant Director and Head of High Energy, Cosmology and Astroparticle Physics Section at the International Centre for Theoretical Physics.
He received his PhD in 1980 from Imperial College London, University of London, UK. Seifallah Randjbar-Daemi's contributions are in the area of theoretical high energy physics, quantum field theory, superstring theory, supersymmetry and supergravity theories in all dimensions and cosmology.
Sheldon Lee GlashowSheldon Lee Glashow (; born December 5, 1932) is a Nobel Prize winning American theoretical physicist. He is the Metcalf Professor of Mathematics and Physics at Boston University and Eugene Higgins Professor of Physics, Emeritus, at Harvard University, and is a member of the Board of Sponsors for the Bulletin of the Atomic Scientists.
String dualityString duality is a class of symmetries in physics that link different string theories, theories which assume that the fundamental building blocks of the universe are strings instead of point particles.
Super Virasoro algebraIn mathematical physics, a super Virasoro algebra is an extension of the Virasoro algebra to a Lie superalgebra. There are two extensions with particular importance in superstring theory: the Ramond algebra (named after Pierre Ramond) and the Neveu–Schwarz algebra (named after André Neveu and John Henry Schwarz). Both algebras have N=1 supersymmetry and an even part given by the Virasoro algebra. They describe the symmetries of a superstring in two different sectors, called the Ramond sector and the Neveu–Schwarz sector.
Sylvester James GatesSylvester James Gates Jr. (born December 15, 1950), known as S. James Gates the 6th or Jim Gates, is an American theoretical physicist who works on supersymmetry, supergravity, and superstring theory. He retired from the physics department at the University of Maryland College of Computer, Mathematical, and Natural Sciences in 2017, and he is now the Ford Foundation Professor of Physics at Brown University. He was a University of Maryland Regents Professor and served on former President Barack Obama's Council of Advisors on Science and Technology.
Type 0 string theoryThe Type 0 string theory is a less well-known model of string theory. It is a superstring theory in the sense that the worldsheet theory is supersymmetric. However, the spacetime spectrum is not supersymmetric and, in fact, does not contain any fermions at all. In dimensions greater than two, the ground state is a tachyon so the theory is unstable. These properties make it similar to the bosonic string and an unsuitable proposal for describing the world as we observe it, although a GSO projection does get rid of the tachyon and the even G-parity sector of the theory defines a stable string theory. The theory is used sometimes as a toy model for exploring concepts in string theory, notably closed string tachyon condensation. Some other recent interest has involved the two-dimensional Type 0 string which has a non-perturbatively stable matrix model description.
Like the Type II string, different GSO projections result in slightly different theories, Type 0A and Type 0B. The difference lies in which types of Ramond-Ramond fields lie in the massless spectrum.
Type II string theoryIn 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.
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