String theory

Superstring theory Theory String theory Superstrings Bosonic string theory M-theory (simplified) Type I string · Type II string Heterotic string String field theory Holographic principle Image File history File links Size of this preview: 600 × 600 pixelsFull resolution (840 × 840 pixel, file size: 327 KB, MIME type: image/png) I created this image myself to replace Image:Calabi-Yau. ... 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 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. ... Bosonic string theory is the original version of string theory, developed in the late 1960s. ... M-theory is a solution proposed for the unknown theory of everything which would combine all five superstring theories and 11-dimensional supergravity together. ... This article is intended as a generally accessible introduction to the subject. ... In theoretical physics, type I string theory is one of five consistent supersymmetric string theories in ten dimensions. ... In theoretical physics, type II string theory is a unified term that includes both type IIA strings and type IIB strings. ... In physics, a heterotic string is a peculiar mixture (or hybrid) of the bosonic string and the superstring (the adjective heterotic comes from the Greek word heterosis). ... String field theory is a proposal to define string theory in such a way that the background independence is respected. ... The holographic principle is a speculative conjecture about quantum gravity theories, proposed by Gerard t Hooft and improved and promoted by Leonard Susskind, claiming that all of the information contained in a volume of space can be represented by a theory which lives in the boundary of that region. ... Concepts Strings · Branes Calabi–Yau manifold Kac–Moody algebra D-brane E8 Lie group Related Topics Supersymmetry Supergravity Quantum gravity Scientists Witten · Green · Greene · Schwarz · Polchinski · Kaku · Susskind · Vafa · Duff

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String theory is a still developing mathematical approach to theoretical physics, whose original building blocks are one-dimensional extended objects called strings. Unlike the point particles in quantum field theories like the standard model of particle physics, strings interact in a way that is almost uniquely specified by mathematical self-consistency, forming an apparently valid quantum theory of gravity. A string is the fundamental object of study in a branch of theoretical physics called string theory. ... P-branes or branes are terms from quantum superstring theory used to refer to membrane-like structures of one to eleven dimensions that arise in equations of this heavily mathematical theory. ... In mathematics, a Kac–Moody algebra is a Lie algebra, usually infinite-dimensional, that can be defined through a generalized root system. ... In theoretical physics, D-branes are a special class of p-branes, named for the mathematician Johann Dirichlet. ... Graph of E8 Gosset polytope, 42,1 Coxeter-Dynkin diagram: . It features superscript or subscript characters that are substituted or omitted because of technical limitations. ... This article or section is in need of attention from an expert on the subject. ... In theoretical physics, supergravity (supergravity theory) refers to a field theory which combines the two theories of supersymmetry and general relativity. ... Quantum gravity is the field of theoretical physics attempting to unify quantum mechanics, which describes three of the fundamental forces of nature, with general relativity, the theory of the fourth fundamental force: gravity. ... Edward Witten (born August 26, 1951) is an American theoretical physicist and professor at the Institute for Advanced Study. ... There are several people called Michael Green, including: [[Mike Green (web developerwww. ... Brian Greene (born February 9, 1963), is a theoretical physicist and one of the best-known string theorists. ... John Henry Schwarz John Henry Schwarz (born 1941) is an American theoretical physicist. ... Joe Polchinski in Santa Barbara Joseph Polchinski (born on May 16, 1954 in White Plains, New York) is a physicist working on string theory. ... Michio Kaku (加來 道雄 Kaku Michio, born January 24, 1947 in the United States) is an American theoretical physicist, tenured professor, and co-founder of string field theory, a branch of superstring theory. ... Leonard Susskind (born 1940[1]) is the Felix Bloch professor of theoretical physics at Stanford University in the field of string theory and quantum field theory. ... Cumrun Vafa is a leading string theorist from Harvard University where he started as a Harvard Junior Fellow. ... Sir Michael Duff, the bon vivant and society figure, was the son of Sir Robin Duff, 2nd Bt, of Vaynol, and his wife Lady Juliet Lowther, only child of the 4th Earl of Lonsdale and his wife Lady Gwladys Herbert (later Marchioness of Ripon). ... Theoretical physics employs mathematical models and abstractions of physics in an attempt to explain experimental data taken of the natural world. ... A string is the fundamental object of study in a branch of theoretical physics called string theory. ... A point particle is an idealized particle heavily used in physics. ... Quantum field theory (QFT) is the quantum theory of fields. ... The Standard Model of Fundamental Particles and Interactions For the Standard Model in Cryptography, see Standard Model (cryptography). ... Thousands of particles explode from the collision point of two relativistic (100 GeV per nucleon) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ... Quantum gravity is the field of theoretical physics attempting to unify quantum mechanics, which describes three of the fundamental forces of nature, with general relativity, the theory of the fourth fundamental force: gravity. ...

Since its birth as the dual resonance model which described the strongly interacting hadrons as strings, the term string theory has changed to include any of a group of related superstring theories and larger frameworks such as M-theory, which unite them. A shared property of all these theories is the holographic principle. In theoretical physics, the term dual resonance models refers to the early investigation (1968-1974 or so) on strong interactions of the subject that is currently known as string theory. ... A hadron, in particle physics, is a subatomic particle which experiences the nuclear force. ... 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. ... M-theory is a solution proposed for the unknown theory of everything which would combine all five superstring theories and 11-dimensional supergravity together. ... The holographic principle is a speculative conjecture about quantum gravity theories, proposed by Gerard t Hooft and improved and promoted by Leonard Susskind, claiming that all of the information contained in a volume of space can be represented by a theory which lives in the boundary of that region. ...

String theorists have not yet completely described these theories, nor have they determined if or how these theories relate to the physical universe.^[1] The elegance and flexibility of the approach, however, and a number of qualitative similarities with more traditional physical models, have led many physicists to suspect that such a connection is possible. In particular, string theory may be a way to "unify" the known natural forces (gravitational, electromagnetic, weak nuclear and strong nuclear) by describing them with the same set of equations, as described in the theory of everything. On the other hand, the models have been criticized for their inability, thus far, to provide any experimentally testable predictions. A fundamental interaction is a mechanism by which particles interact with each other, and which cannot be explained by another more fundamental interaction. ... Gravity is a force of attraction that acts between bodies that have mass. ... Electromagnetism is the physics of the electromagnetic field: a field which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles. ... The weak interaction (often called the weak force or sometimes the weak nuclear force) is one of the four fundamental interactions of nature. ... The strong interaction or strong force is today understood to represent the interactions between quarks and gluons as detailed by the theory of quantum chromodynamics (QCD). ... This page discusses Theories of Everything in physics. ...

Like any other quantum theory of gravity, it is widely believed that testing the theory experimentally would be prohibitively expensive, requiring heroic feats of engineering on a solar-system scale. Although string theory like any other scientific theory is falsifiable in principle, critics maintain that it is unfalsifiable for the foreseeable future, and so should not be called science.

Work on string theory is made interesting because of the mathematics involved, and because of the large number of forms that the theories can take. String theory strongly suggests that spacetime has eleven dimensions ^[2], not the usual three space and one time; but the theory can easily describe universes with four observable spacetime dimensions too.^[3] For other uses of this term, see Spacetime (disambiguation). ... For other uses of this term, see Spacetime (disambiguation). ...

String theories include higher-dimensional objects than strings, called branes. These are black-holes charged with a differential form vector potential which has more than one index, a different type of electricity and magnetism where the fundamental objects are extended. By studying these p-branes and identifying them with D-branes, endpoints for strings, certain types of string theory are shown to be equivalent to certain types of more traditional gauge theory. Research on this equivalence has led to new insights on quantum chromodynamics, the fundamental theory of the strong nuclear force.^[4][5][6][7] In physics, hyperspace is a theoretical entity. ... P-branes or branes are terms from quantum superstring theory used to refer to membrane-like structures of one to eleven dimensions that arise in equations of this heavily mathematical theory. ... A differential form is a mathematical concept in the fields of multivariate calculus, differential topology and tensors. ... In vector calculus, a vector potential is a vector field whose curl is a given vector field. ... In theoretical physics, D-branes are a special class of p-branes, named for the physicist Johann Dirichlet. ... This box:      String theory is a still developing mathematical approach to theoretical physics, whose original building blocks are one-dimensional extended objects called strings. ... In physics, gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... Quantum chromodynamics (abbreviated as QCD) is the theory of the strong interaction (color force), a fundamental force describing the interactions of the quarks and gluons found in hadrons (such as the proton, neutron or pion). ... The strong interaction or strong force is today understood to represent the interactions between quarks and gluons as detailed by the theory of quantum chromodynamics (QCD). ...

Overview

For more details on why it is hard to unite gravity and quantum physics, and on alternatives to string theory, see quantum gravity.

Matter is composed of atoms, which in turn are made from quarks and electrons. According to String theory, all such particles are actually tiny loops or segments of vibrating string ^[8]. The idea behind all string theories is that each elementary "particle" is actually a string of a very small scale (possibly of the order of the Planck length) which vibrates at resonant frequencies specific to that type of particle.^[9] Thus, any elementary particle should be thought of as a tiny vibrating object, rather than as a point. This object can vibrate in different modes (just as a guitar string can produce different notes), with every mode appearing as a different particle (electron, photon, etc.). Strings can split and combine, which would appear as particles emitting and absorbing other particles, presumably giving rise to the known interactions between particles. Quantum gravity is the field of theoretical physics attempting to unify quantum mechanics, which describes three of the fundamental forces of nature, with general relativity, the theory of the fourth fundamental force: gravity. ... For the novel, see The Elementary Particles. ... A string is the fundamental object of study in a branch of theoretical physics called string theory. ... The Planck length, denoted by , is the unit of length approximately 1. ... This article is about resonance in physics. ... For other uses, see Frequency (disambiguation). ... For the novel, see The Elementary Particles. ... For other uses, see Electron (disambiguation). ... In modern physics the photon is the elementary particle responsible for electromagnetic phenomena. ... A fundamental interaction or fundamental force is a mechanism by which particles interact with each other, and which cannot be explained in terms of another interaction. ...

Levels of magnification: Macroscopic level, molecular level, atomic level, subatomic level, string level.

In addition to strings, this theory also includes objects of higher dimensions, such as D-branes and NS-branes. Furthermore, all string theories predict the existence of degrees of freedom which are usually described as extra dimensions. String theory is thought to include some 10, 11, or 26 dimensions, depending on the specific theory and on the point of view. Image File history File links Size of this preview: 800 × 290 pixelsFull resolution‎ (1,197 × 434 pixels, file size: 142 KB, MIME type: image/png) Other versions / File historyClick on a date/time to view the file as it appeared at that time. ... Image File history File links Size of this preview: 800 × 290 pixelsFull resolution‎ (1,197 × 434 pixels, file size: 142 KB, MIME type: image/png) Other versions / File historyClick on a date/time to view the file as it appeared at that time. ... In theoretical physics, D-branes are a special class of p-branes, named for the mathematician Johann Dirichlet. ... In theoretical physics, an NS5-brane is a five-dimensional object (a p-brane) in string theory that carries a magnetic charge under the B-field, the field under which the fundamental string is electrically charged. ... Degrees of freedom is a general term used in explaining dependence on parameters, and implying the possibility of counting the number of those parameters. ... This box:      String theory is a still developing mathematical approach to theoretical physics, whose original building blocks are one-dimensional extended objects called strings. ...

Interest in string theory is driven largely by the hope that it will prove to be a consistent theory of quantum gravity or even a theory of everything. It can also naturally describe interactions similar to electromagnetism and the other forces of nature. Superstring theories include fermions, the building blocks of matter, and incorporate supersymmetry, a conjectured (but unobserved) symmetry of nature. It is not yet known whether string theory will be able to describe a universe with the precise collection of forces and particles that is observed, nor how much freedom the theory allows to choose those details. Quantum gravity is the field of theoretical physics attempting to unify quantum mechanics, which describes three of the fundamental forces of nature, with general relativity, the theory of the fourth fundamental force: gravity. ... This page discusses Theories of Everything in physics. ... Electromagnetism is the physics of the electromagnetic field: a field which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles. ... 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. ... In particle physics, fermions are particles with half-integer spin, such as protons and electrons. ... This article is about matter in physics and chemistry. ... This article or section is in need of attention from an expert on the subject. ... This article or section does not cite its references or sources. ... For other uses, see Universe (disambiguation). ...

String theory as a whole has not yet made practically falsifiable predictions that would allow it to be experimentally tested, though various planned observations and experiments could confirm some essential aspects of the theory, such as supersymmetry and extra dimensions. In addition, the full theory is not yet understood. For example, the theory does not yet have a satisfactory definition outside of perturbation theory; the quantum mechanics of branes (higher dimensional objects than strings) is not understood; the behavior of string theory in cosmological settings (time-dependent backgrounds) is still being worked out; finally, the principle by which string theory selects its vacuum state is a hotly contested topic (see string theory landscape). Falsifiability (or refutability or testability) is the logical possibility that an assertion can be shown false by an observation or a physical experiment. ... In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. ... For a generally accessible and less technical introduction to the topic, see Introduction to quantum mechanics. ... In quantum field theory, the vacuum state, usually denoted , is the element of the Hilbert space with the lowest possible energy, and therefore containing no physical particles. ... The string theory landscape or anthropic landscape refers to the large number of different false vacua in string theory. ...

String theory is thought to be a certain limit of another, more fundamental theory — M-theory — which is only partly defined and is not well understood.^[10] M-theory is a solution proposed for the unknown theory of everything which would combine all five superstring theories and 11-dimensional supergravity together. ...

Basic properties

String theory is formulated in terms of an action principle, either the Nambu-Goto action or the Polyakov action, which describes how strings move through space and time. Like springs with no external force applied, the strings tend to shrink, thus minimizing their potential energy, but conservation of energy prevents them from disappearing, and instead they oscillate. By applying the ideas of quantum mechanics to strings it is possible to deduce the different vibrational modes of strings, and that each vibrational state appears to be a different particle. The mass of each particle, and the fashion in which it can interact, are determined by the way the string vibrates — the string can vibrate in many different modes, just like a guitar string can produce different notes. The different modes, each corresponding to a different kind of particle, make up the "spectrum" of the theory. In physics, the action is an integral quantity that is used to determine the evolution of a physical system between two defined states using the calculus of variations. ... The Nambu-Goto action is the simplest invariant action in bosonic string theory. ... In physics, the Polyakov action is the two-dimensional action of a conformal field theory describing the worldsheet of a string in string theory. ... This article is about the law of conservation of energy in physics. ... For a generally accessible and less technical introduction to the topic, see Introduction to quantum mechanics. ... This article needs to be cleaned up to conform to a higher standard of quality. ...

Strings can split and combine, which would appear as particles emitting and absorbing other particles, presumably giving rise to the known interactions between particles.

String theory includes both open strings, which have two distinct endpoints, and closed strings, where the endpoints are joined to make a complete loop. The two types of string behave in slightly different ways, yielding two different spectra. For example, in most string theories, one of the closed string modes is the graviton, and one of the open string modes is the photon. Because the two ends of an open string can always meet and connect, forming a closed string, there are no string theories without closed strings. A string is the fundamental object of study in a branch of theoretical physics called string theory. ... This article is about the hypothetical particle. ... In modern physics the photon is the elementary particle responsible for electromagnetic phenomena. ...

The earliest string model — the bosonic string, which incorporated only bosons, describes — in low enough energies — a quantum gravity theory, which also includes (if open strings are incorporated as well) gauge fields such as the photon (or, more generally, any gauge theory). However, this model has problems. Most importantly, the theory has a fundamental instability, believed to result in the decay (at least partially) of space-time itself. Additionally, as the name implies, the spectrum of particles contains only bosons, particles which, like the photon, obey particular rules of behavior. Roughly speaking, bosons are the constituents of radiation, but not of matter, which is made of fermions. Investigating how a string theory may include fermions in its spectrum led to the invention of supersymmetry, a mathematical relation between bosons and fermions. String theories which include fermionic vibrations are now known as superstring theories; several different kinds have been described, but all are now thought to be different limits of M-theory. Bosonic string theory is the original version of string theory, developed in the late 1960s. ... In particle physics, bosons are particles with an integer spin, as opposed to fermions which have half-integer spin. ... Gravity is a force of attraction that acts between bodies that have mass. ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... In physics, gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... In particle physics, fermions are particles with half-integer spin, such as protons and electrons. ... This article or section is in need of attention from an expert on the subject. ... 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. ... M-theory is a solution proposed for the unknown theory of everything which would combine all five superstring theories and 11-dimensional supergravity together. ...

Some qualitative properties of quantum strings can be understood in a fairly intuitive fashion. For example, quantum strings have tension, much like regular strings made of twine; this tension is considered a fundamental parameter of the theory. The tension of a quantum string is closely related to its size. Consider a closed loop of string, left to move through space without external forces. Its tension will tend to contract it into a smaller and smaller loop. Classical intuition suggests that it might shrink to a single point, but this would violate Heisenberg's uncertainty principle. The characteristic size of the string loop will be a balance between the tension force, acting to make it small, and the uncertainty effect, which keeps it "stretched". Consequently, the minimum size of a string is related to the string tension. A spool of twine. ... Werner Karl Heisenberg (December 5, 1901 – February 1, 1976) was a celebrated German physicist and Nobel laureate, one of the founders of quantum mechanics and acknowledged to be one of the most important physicists of the twentieth century. ... In quantum physics, the outcome of even an ideal measurement of a system is not deterministic, but instead is characterized by a probability distribution, and the larger the associated standard deviation is, the more uncertain we might say that that characteristic is for the system. ...

Worldsheet

For more details on this topic, see Relationship between string theory and quantum field theory.

A point-like particle's motion may be described by drawing a graph of its position (in one or two dimensions of space) against time. The resulting picture depicts the worldline of the particle (its 'history') in spacetime. By analogy, a similar graph depicting the progress of a string as time passes by can be obtained; the string (a one-dimensional object — a small line — by itself) will trace out a surface (a two-dimensional manifold), known as the worldsheet. The different string modes (representing different particles, such as photon or graviton) are surface waves on this manifold. Many first principles in quantum field theory are explained, or get further insight, in string theory: Emission and absorption: one of the most basic building blocks of quantum field theory, is the notion that particles (such as electrons) can emit and absorb other particles (such as photons). ... A world line of an object or person is the sequence of events labeled with time and place, that marks the history of the object or person. ... For other uses of this term, see Spacetime (disambiguation). ... On a sphere, the sum of the angles of a triangle is not equal to 180° (see spherical trigonometry). ... A world line of an object or person is the sequence of events labeled with time and place, that marks the history of the object or person. ... In modern physics the photon is the elementary particle responsible for electromagnetic phenomena. ... This article is about the hypothetical particle. ...

A closed string looks like a small loop, so its worldsheet will look like a pipe, or — more generally — as a Riemannian surface (a two-dimensional oriented manifold) with no boundaries (i.e. no edge). An open string looks like a short line, so its worldsheet will look like a strip, or — more generally — as a Riemann surface with a boundary. A string is the fundamental object of study in a branch of theoretical physics called string theory. ... Riemann surface for the function f(z) = sqrt(z) In mathematics, particularly in complex analysis, a Riemann surface, named after Bernhard Riemann, is a one-dimensional complex manifold. ... The torus is an orientable surface. ... Riemann surface for the function f(z) = sqrt(z) In mathematics, particularly in complex analysis, a Riemann surface, named after Bernhard Riemann, is a one-dimensional complex manifold. ...

Interaction in the subatomic world: world lines of point-like particles in the Standard Model or a world sheet swept up by closed strings in string theory

Strings can split and connect. This is reflected by the form of their worldsheet (more accurately, by its topology). For example, if a closed string splits, its worldsheet will look like a single pipe splitting (or connected) to two pipes (often referred to as a pair of pants — see drawing at right). If a closed string splits and its two parts later reconnect, its worldsheet will look like a single pipe splitting to two and then reconnecting, which also looks like a torus connected to two pipes (one representing the ingoing string, and the other — the outgoing one). An open string doing the same thing will have its worldsheet looking like a ring connected to two strips. Image File history File links Point&string. ... Image File history File links Point&string. ... In physics, the world line of an object is the unique path of that object as it travels through 4-dimensional spacetime. ... Helium atom (schematic) Showing two protons (red), two neutrons (green) and two electrons (yellow). ... The Standard Model of Fundamental Particles and Interactions For the Standard Model in Cryptography, see Standard Model (cryptography). ... A world line of an object or person is the sequence of events labeled with time and place, that marks the history of the object or person. ... A string is the fundamental object of study in a branch of theoretical physics called string theory. ... A Möbius strip, an object with only one surface and one edge; such shapes are an object of study in topology. ... In geometry, a torus (pl. ...

Note that the process of a string splitting (or strings connecting) is a global process of the worldsheet, not a local one: locally, the worldsheet looks the same everywhere and it is not possible to determine a single point on the worldsheet where the splitting occurs. Therefore these processes are an integral part of the theory, and are described by the same dynamics that controls the string modes.

In some string theories (namely, closed strings in Type I and some versions of the bosonic string), strings can split and reconnect in an opposite orientation (as in a Möbius strip or a Klein bottle). These theories are called unoriented. Formally, the worldsheet in these theories is a non-orientable surface. In theoretical physics, type I string theory is one of five consistent supersymmetric string theories in ten dimensions. ... Bosonic string theory is the original version of string theory, developed in the late 1960s. ... A Möbius strip made with a piece of paper and tape. ... The Klein bottle immersed in three-dimensional space. ... The torus is an orientable surface. ...

Dualities

Main articles: String duality, S-duality, T-duality, and U-duality

Before the 1990s, string theorists believed there were five distinct superstring theories: type I, types IIA and IIB, and the two heterotic string theories (SO(32) and E₈×E₈). The thinking was that out of these five candidate theories, only one was the actual correct theory of everything, and that theory was the one whose low energy limit, with ten spacetime dimensions compactified down to four, matched the physics observed in our world today. It is now known that this picture was naïve, and that the five superstring theories are connected to one another as if they are each a special case of some more fundamental theory (thought to be M-theory). These theories are related by transformations that are called dualities. If two theories are related by a duality transformation, it means that the first theory can be transformed in some way so that it ends up looking just like the second theory. The two theories are then said to be dual to one another under that kind of transformation. Put differently, the two theories are mathematically different descriptions of the same phenomena. String duality is a type of symmetry in physics that links different string theories, theories which assume that the fundamental building blocks of the universe are strings instead of point particles. ... In theoretical physics, S-duality (also a strong-weak duality) is an equivalence of two quantum field theories, string theories, or M-theory. ... T-duality is a symmetry of string theory, relating type IIA and type IIB string theory, and the two heterotic string theories. ... U-duality is a symmetry of string theory or M-theory combining S-duality and T-duality transformations. ... In theoretical physics, type I string theory is one of five consistent supersymmetric string theories in ten dimensions. ... In theoretical physics, type II string theory is a unified term that includes both type IIA strings and type IIB strings. ... In theoretical physics, type II string theory is a unified term that includes both type IIA strings and type IIB strings. ... In physics, a heterotic string is a peculiar mixture (or hybrid) of the bosonic string and the superstring (the adjective heterotic comes from the Greek word heterosis). ... In mathematics, the orthogonal group of degree n over a field F (written as O(n,F)) is the group of n-by-n orthogonal matrices with entries from F, with the group operation that of matrix multiplication. ... Graph of E8 Gosset polytope, 42,1 Coxeter-Dynkin diagram: . It features superscript or subscript characters that are substituted or omitted because of technical limitations. ... This page discusses Theories of Everything in physics. ... In physics, compactification plays an important part in string theory. ... M-theory is a solution proposed for the unknown theory of everything which would combine all five superstring theories and 11-dimensional supergravity together. ...

These dualities link quantities that were also thought to be separate. Large and small distance scales, as well as strong and weak coupling strengths, are quantities that have always marked very distinct limits of behavior of a physical system in both classical field theory and quantum particle physics. But strings can obscure the difference between large and small, strong and weak, and this is how these five very different theories end up being related. T-duality relates the large and small distance scales between string theories, whereas S-duality relates strong and weak coupling strengths between string theories. U-duality links T-duality and S-duality. Field theory (mathematics), the theory of the algebraic concept of field. ... Thousands of particles explode from the collision point of two relativistic (100 GeV per nucleon) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ...

Before the "duality revolution" there were believed to be five distinct versions of string theory, plus the (unstable) bosonic and gluonic theories.

Note that in the type IIA and type IIB string theories closed strings are allowed to move everywhere throughout the ten-dimensional space-time (called the bulk), while open strings have their ends attached to D-branes, which are membranes of lower dimensionality (their dimension is odd — 1,3,5,7 or 9 — in type IIA and even — 0,2,4,6 or 8 — in type IIB, including the time direction). In particle physics, bosons are particles with an integer spin, as opposed to fermions which have half-integer spin. ... In particle physics, fermions are particles with half-integer spin, such as protons and electrons. ... Thousands of particles explode from the collision point of two relativistic (100 GeV per nucleon) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ... A tachyon (from the Greek (takhús), meaning swift, fast) is any hypothetical particle that travels at superluminal velocity. ... This article or section is in need of attention from an expert on the subject. ... A tachyon (from the Greek (takhús), meaning swift, fast) is any hypothetical particle that travels at superluminal velocity. ... In mathematics, the orthogonal group of degree n over a field F (written as O(n,F)) is the group of n-by-n orthogonal matrices with entries from F, with the group operation that of matrix multiplication. ... This article or section is in need of attention from an expert on the subject. ... In theoretical physics, D-branes are a special class of p-branes, named for the mathematician Johann Dirichlet. ... A tachyon (from the Greek (takhús), meaning swift, fast) is any hypothetical particle that travels at superluminal velocity. ... In particle physics, fermions are particles with half-integer spin, such as protons and electrons. ... This article or section is in need of attention from an expert on the subject. ... In theoretical physics, D-branes are a special class of p-branes, named for the mathematician Johann Dirichlet. ... A tachyon (from the Greek (takhús), meaning swift, fast) is any hypothetical particle that travels at superluminal velocity. ... In particle physics, fermions are particles with half-integer spin, such as protons and electrons. ... This article or section is in need of attention from an expert on the subject. ... A tachyon (from the Greek (takhús), meaning swift, fast) is any hypothetical particle that travels at superluminal velocity. ... In physics, a heterotic string is a peculiar mixture (or hybrid) of the bosonic string and the superstring (the adjective heterotic comes from the Greek word heterosis). ... In mathematics, the orthogonal group of degree n over a field F (written as O(n,F)) is the group of n-by-n orthogonal matrices with entries from F, with the group operation that of matrix multiplication. ... This article or section is in need of attention from an expert on the subject. ... A tachyon (from the Greek (takhús), meaning swift, fast) is any hypothetical particle that travels at superluminal velocity. ... In physics, a heterotic string is a peculiar mixture (or hybrid) of the bosonic string and the superstring (the adjective heterotic comes from the Greek word heterosis). ... Graph of E8 Gosset polytope, 42,1 Coxeter-Dynkin diagram: . It features superscript or subscript characters that are substituted or omitted because of technical limitations. ... In theoretical physics, D-branes are a special class of p-branes, named for the mathematician Johann Dirichlet. ...

Extra dimensions

Number of dimensions

An intriguing feature of string theory is that it involves the prediction of extra dimensions. The number of dimensions is not fixed by any consistency criterion, but flat spacetime solutions do exist in the so-called "critical dimension." Cosmological solutions exist in a wider variety of dimensionalities, and these different dimensions—more precisely different values of the "effective central charge," a count of degrees of freedom which reduces to dimensionality in weakly curved regimes—are related by dynamical transitions.^[11] In physics and mathematics, Minkowski space (or Minkowski spacetime) is the mathematical setting in which Einsteins theory of special relativity is most conveniently formulated. ...

Nothing in Maxwell's theory of electromagnetism or Einstein's theory of relativity makes this kind of prediction; these theories require physicists to insert the number of dimensions "by hand," and this number is fixed and independent of potential energy. String theory allows one to relate the number of dimensions to scalar potential energy. Technically, this happens because a gauge anomaly exists for every separate number of predicted dimensions, and the gauge anomaly can be counteracted by including nontrivial potential energy into equations to solve motion. Furthermore, the absence of potential energy in the "critical dimension" explains why flat spacetime solutions are possible. James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and theoretical physicist. ... Electromagnetism is the physics of the electromagnetic field: a field which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles. ... “Einstein” redirects here. ... Two-dimensional analogy of space-time curvature described in General Relativity. ... In theoretical physics, a gauge anomaly is an example of an anomaly: it is an effect of quantum mechanics - usually a one-loop diagram - that invalidates the gauge symmetry of a quantum field theory i. ...

This can be better understood by noting that a photon included in a consistent theory (technically, a particle carrying a force related to an unbroken gauge symmetry) must be massless. The mass of the photon which is predicted by string theory depends on the energy of the string mode which represents the photon. This energy includes a contribution from the Casimir effect, namely from quantum fluctuations in the string. The size of this contribution depends on the number of dimensions since for a larger number of dimensions, there are more possible fluctuations in the string position. Therefore, the photon in flat spacetime will be massless—and the theory consistent—only for a particular number of dimensions.^[12] In modern physics the photon is the elementary particle responsible for electromagnetic phenomena. ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... The term mass in special relativity is used in a couple of different ways, occasionally leading to a great deal of confusion. ... In physics, the Casimir effect is a physical force exerted between separate objects, which is due to neither charge, gravity, nor the exchange of particles, but instead is due to resonance of all-pervasive energy fields in the intervening space between the objects. ...

When the calculation is done, the critical dimensionality is not four as one may expect (three axes of space and one of time). Flat space string theories are 26-dimensional in the bosonic case, while superstring and M-theories turn out to involve 10 or 11 dimensions for flat solutions. In bosonic string theories, the 26 dimensions come from the Polyakov equation.^[13] Starting from any dimension greater than four, it is necessary to consider how these are reduced to four dimensional space-time. In special relativity and general relativity, time and three-dimensional space are treated together as a single four-dimensional pseudo-Riemannian manifold called spacetime. ...

Calabi-Yau manifold (3D projection)

Image File history File links Size of this preview: 600 × 600 pixelsFull resolution (840 × 840 pixel, file size: 327 KB, MIME type: image/png) I created this image myself to replace Image:Calabi-Yau. ... Image File history File links Size of this preview: 600 × 600 pixelsFull resolution (840 × 840 pixel, file size: 327 KB, MIME type: image/png) I created this image myself to replace Image:Calabi-Yau. ... Calabi-Yau manifold (an artists impression) In mathematics, a Calabi-Yau manifold is a compact Kähler manifold with a vanishing first Chern class. ... A 3D projection is a mathematical transformation used to project three dimensional points onto a two dimensional plane[1]. Often this is done to simulate the relationship of a camera to a subject, as 3D projection is often the first step in the process of representing three dimensional shapes two...

Compact dimensions

Two different ways have been proposed to resolve this apparent contradiction. The first is to compactify the extra dimensions; i.e., the 6 or 7 extra dimensions are so small as to be undetectable in our phenomenal experience. In order to retain the supersymmetric properties of string theory, these spaces must be very special. The 6-dimensional model's resolution is achieved with Calabi-Yau spaces. In 7 dimensions, they are termed G₂ manifolds. These extra dimensions are compactified by causing them to loop back upon themselves. In statistics, dimensionality reduction can be divided into two categories: feature selection and feature extraction. ... In mathematics, a Calabi-Yau manifold is a compact Kähler manifold with a vanishing first Chern class. ... The title given to this article is incorrect due to technical limitations. ...

A standard analogy for this is to consider multidimensional space as a garden hose. If the hose is viewed from a sufficient distance, it appears to have only one dimension, its length. Indeed, think of a ball just small enough to enter the hose. Throwing such a ball inside the hose, the ball would move more or less in one dimension; in any experiment we make by throwing such balls in the hose, the only important movement will be one-dimensional, that is, along the hose. However, as one approaches the hose, one discovers that it contains a second dimension, its circumference. Thus, an ant crawling inside it would move in two dimensions (and a fly flying in it would move in three dimensions). This "extra dimension" is only visible within a relatively close range to the hose, or if one "throws in" small enough objects. Similarly, the extra compact dimensions are only "visible" at extremely small distances, or by experimenting with particles with extremely small wavelengths (of the order of the compact dimension's radius), which in quantum mechanics means very high energies (see wave-particle duality). For other uses, see Wavelength (disambiguation). ... For a generally accessible and less technical introduction to the topic, see Introduction to quantum mechanics. ... In physics, wave-particle duality holds that light and matter exhibit properties of both waves and of particles. ...

Brane-world scenario

Another possibility is that we are "stuck" in a 3+1 dimensional (i.e. three spatial dimensions plus the time dimension) subspace of the full universe. This subspace is supposed to be a D-brane, hence this is known as a braneworld theory. Many people believe that some combination of the two ideas — compactification and branes — will ultimately yield the most realistic theory.^{[citation needed]} In theoretical physics, D-branes are a special class of p-branes, named for the mathematician Johann Dirichlet. ... Brane cosmology is a protoscience motivated by, but not rigorously derived from, superstring theory and M-theory. ...

Effect of the hidden dimensions

In either case, gravity acting in the hidden dimensions affects other non-gravitational forces such as electromagnetism. In fact, Kaluza and Klein's early work demonstrated that general relativity with four large dimensions and one small dimension actually predicts the existence of electromagnetism. However, because of the nature of Calabi-Yau manifolds, no new forces appear from the small dimensions, but their shape has a profound effect on how the forces between the strings appear in our four dimensional universe. In principle, therefore, it is possible to deduce the nature of those extra dimensions by requiring consistency with the standard model, but this is not yet a practical possibility. It is also possible to extract information regarding the hidden dimensions by precision tests of gravity, but so far these have only put upper limitations on the size of such hidden dimensions. Calabi-Yau manifold (an artists impression) In mathematics, a Calabi-Yau manifold is a compact Kähler manifold with a vanishing first Chern class. ... The Standard Model of Fundamental Particles and Interactions For the Standard Model in Cryptography, see Standard Model (cryptography). ...

D-branes

Main article: D-brane

Another key feature of string theory is the existence of D-branes. These are membranes of different dimensionality (anywhere from a zero dimensional membrane — which is in fact a point — and up, including 2-dimensional membranes, 3-dimensional volumes and so on). In theoretical physics, D-branes are a special class of p-branes, named for the mathematician Johann Dirichlet. ...

D-branes are defined by the fact that worldsheet boundaries are attached to them. Thus D-branes can emit and absorb closed strings; therefore they have mass (since they emit gravitons) and — in superstring theories — charge as well (since they emit closed strings which are gauge bosons). A world line of an object or person is the sequence of events labeled with time and place, that marks the history of the object or person. ... In topology, the boundary of a subset S of a topological space X is the set of points which can be approached both from S and from the outside of S. More formally, it is the set of points in the closure of S, not belonging to the interior of... This article is about the hypothetical particle. ... 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. ... In physics, a charge may refer to one of many different quantities, such as the electric charge in electromagnetism or the color charge in quantum chromodynamics. ...

From the point of view of open strings, D-branes are objects to which the ends of open strings are attached. The open strings attached to a D-brane are said to "live" on it, and they give rise to gauge theories "living" on it (since one of the open string modes is a gauge boson such as the photon). In the case of one D-brane there will be one type of a gauge boson and we will have an Abelian gauge theory (with the gauge boson being the photon). If there are multiple parallel D-branes there will be multiple types of gauge bosons, giving rise to a non-Abelian gauge theory. In physics, gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... Gauge bosons are bosonic particles which act as carriers of the fundamental forces of Nature. ... In mathematics, an abelian group, also called a commutative group, is a group (G, * ) with the additional property that * commutes: for all a and b in G, a * b = b * a. ... In modern physics the photon is the elementary particle responsible for electromagnetic phenomena. ... In mathematics, an abelian group, also called a commutative group, is a group (G, *) such that a * b = b * a for all a and b in G. Abelian groups are named after Niels Henrik Abel. ...

D-branes are thus gravitational sources, on which a gauge theory "lives". This gauge theory is coupled to gravity (which is said to exist in the bulk), so that normally each of these two different viewpoints is incomplete. In physics, two systems are coupled if they are interacting with each other. ... Gravity is a force of attraction that acts between bodies that have mass. ...

Gauge-gravity duality

Gauge-gravity duality is a conjectured duality between a quantum theory of gravity in certain cases and gauge theory in a lower number of dimensions. This means that each predicted phenomenon and quantity in one theory has an analogue in the other theory, with a "dictionary" translating from one theory to the other. In physics, gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ...

Description of the duality

In certain cases the gauge theory on the D-branes is decoupled from the gravity living in the bulk; thus open strings attached to the D-branes are not interacting with closed strings. Such a situation is termed a decoupling limit. In physics, gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... In physics, two systems are coupled if they are interacting with each other. ... Gravity is a force of attraction that acts between bodies that have mass. ... A fundamental interaction or fundamental force is a mechanism by which particles interact with each other, and which cannot be explained in terms of another interaction. ...

In those cases, the D-branes have two independent alternative descriptions. As discussed above, from the point of view of closed strings, the D-branes are gravitational sources, and thus we have a gravitational theory on spacetime with some background fields. From the point of view of open strings, the physics of the D-branes is described by the appropriate gauge theory. Therefore in such cases it is often conjectured that the gravitational theory on spacetime with the appropriate background fields is dual (i.e. physically equivalent) to the gauge theory on the boundary of this spacetime (since the subspace filled by the D-branes is the boundary of this spacetime). So far, this duality has not been proven in any cases, so there is also disagreement among string theorists regarding how strong the duality applies to various models. In theoretical physics, D-branes are a special class of p-branes, named for the mathematician Johann Dirichlet. ...

Examples and intuition

The most well-known example and the first one to be studied is the duality between Type IIB supergravity on AdS⁵ S⁵ (a product space of a five-dimensional Anti de Sitter space and a five-sphere) on one hand, and N = 4 supersymmetric Yang-Mills theory on the four-dimensional boundary of the Anti de Sitter space (either a flat four-dimensional spacetime R^3,1 or a three-sphere with time S³ R).^[14] This is known as the AdS/CFT correspondence, a name often used for Gauge / gravity duality in general. In theoretical physics, supergravity (supergravity theory) refers to a field theory which combines the two theories of supersymmetry and general relativity. ... In topology, the cartesian product of topological spaces is turned into a topological space in the following way. ... In mathematics and physics, n-dimensional anti de Sitter space, denoted , is the maximally symmetric, simply-connected, Lorentzian manifold with constant negative curvature. ... This article or section is in need of attention from an expert on the subject. ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... For other uses, see Sphere (disambiguation). ... In physics, the AdS/CFT correspondence (anti-de-Sitter space/conformal field theory correspondence), sometimes called the Maldacena duality, is the conjectured equivalence between a string theory defined on one space, and a quantum field theory without gravity defined on the conformal boundary of this space, whose dimension is lower...

This duality can be thought of as follows: suppose there is a spacetime with a gravitational source, for example an extremal black hole. When particles are far away from this source, they are described by closed strings (i.e. a gravitational theory, or usually supergravity). As the particles approach the gravitational source, they can still be described by closed strings; alternatively, they can be described by objects similar to QCD strings, which are made of gauge bosons (gluons) and other gauge theory degrees of freedom. So if one is able (in a decoupling limit) to describe the gravitational system as two separate regions — one (the bulk) far away from the source, and the other close to the source — then the latter region can also be described by a gauge theory on D-branes. This latter region (close to the source) is termed the near-horizon limit, since usually there is an event horizon around (or at) the gravitational source. In theoretical physics, an extremal black hole is a black hole with the minimal possible mass that can be compatible with the given charges and angular momentum. ... In theoretical physics, supergravity (supergravity theory) refers to a field theory which combines the two theories of supersymmetry and general relativity. ... In quantum chromodynamics, or more generally, quantum gauge theories with a connection which are confining, stringlike degrees of freedom called QCD strings or QCD flux tubes form. ... Gauge bosons are bosonic particles which act as carriers of the fundamental forces of Nature. ... In particle physics, gluons are subatomic particles that cause quarks to interact, and are indirectly responsible for the binding of protons and neutrons together in atomic nuclei. ... In physics, gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... For the science fiction film, see Event Horizon (film). ...

In the gravitational theory, one of the directions in spacetime is the radial direction, going from the gravitational source and away (towards the bulk). The gauge theory lives only on the D-brane itself, so it does not include the radial direction: it lives in a spacetime with one less dimension compared to the gravitational theory (in fact, it lives on a spacetime identical to the boundary of the near-horizon gravitational theory). Let us understand how the two theories are still equivalent:

The physics of the near-horizon gravitational theory involves only on-shell states (as usual in string theory), while the field theory includes also off-shell correlation function. The on-shell states in the near-horizon gravitational theory can be thought of as describing only particles arriving from the bulk to the near-horizon region and interacting there between themselves. In the gauge theory these are "projected" onto the boundary, so that particles which arrive at the source from different directions will be seen in the gauge theory as (off-shell) quantum fluctuations far apart from each other, while particles arriving at the source from almost the same direction in space will be seen in the gauge theory as (off-shell) quantum fluctuations close to each other. Thus the angle between the arriving particles in the gravitational theory translates to the distance scale between quantum fluctuations in the gauge theory. The angle between arriving particles in the gravitational theory is related to the radial distance from the gravitational source at which the particles interact: the larger the angle, the closer the particles have to get to the source in order to interact with each other. On the other hand, the scale of the distance between quantum fluctuations in a quantum field theory is related (inversely) to the energy scale in this theory. So small radius in the gravitational theory translates to low energy scale in the gauge theory (i.e. the IR regime of the field theory) while large radius in the gravitational theory translates to high energy scale in the gauge theory (i.e. the UV regime of the field theory). In physics, particularly in classical field theory, configurations of a physical system that satisfy classical equations of motion are called on shell, and those that do not are called off shell. ... Field theory (mathematics), the theory of the algebraic concept of field. ... In physics, particularly in classical field theory, configurations of a physical system that satisfy classical equations of motion are called on shell, and those that do not are called off shell. ... For stochastic processes, including those that arise in statistical mechanics and Euclidean quantum field theory, a correlation function is the correlation between random variables at two different points in space or time. ... Quantum field theory (QFT) is the quantum theory of fields. ... Field theory (mathematics), the theory of the algebraic concept of field. ... In physics, gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ...

A simple example to this principle is that if in the gravitational theory there is a setup in which the dilaton field (which determines the strength of the coupling) is decreasing with the radius, then its dual field theory will be asymptotically free, i.e. its coupling will grow weaker in high energies. In theoretical physics, dilaton originally referred to a theoretical scalar field; as a photon refers in one sense to the electromagnetic field. ... In physics, two systems are coupled if they are interacting with each other. ... In physics, asymptotic freedom is the property of some gauge theories in which the interaction between the particles, such as quarks, becomes arbitrarily weak at ever shorter distances, i. ...

Contact with experiment

This branch of string theory may lead to new insights on quantum chromodynamics, a gauge theory which is the fundamental theory of the strong nuclear force. To this end, it is hoped that a gravitational theory dual to quantum chromodynamics will be found.^[15] Quantum chromodynamics (abbreviated as QCD) is the theory of the strong interaction (color force), a fundamental force describing the interactions of the quarks and gluons found in hadrons (such as the proton, neutron or pion). ... The strong interaction or strong force is today understood to represent the interactions between quarks and gluons as detailed by the theory of quantum chromodynamics (QCD). ...