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Heterotic String Theory
In string theory, a heterotic string is a closed string (or loop) which is a hybrid ('heterotic') of a superstring and a bosonic string. There are two kinds of heterotic string, the heterotic SO(32) and the heterotic E8 × E8, abbreviated to HO and HE. Heterotic string theory was first developed in 1985 by David Gross, Jeffrey Harvey, Emil Martinec, and Ryan Rohm (the so-called "Princeton string quartet"), in one of the key papers that fueled the first superstring revolution. Overview In string theory, the left-moving and the right-moving excitations are completely decoupled, and it is possible to construct a string theory whose left-moving (counter-clockwise) excitations are treated as a bosonic string propagating in ''D'' = 26 dimensions, while the right-moving (clockwise) excitations are treated as a superstring in ''D'' = 10 dimensions. The mismatched 16 dimensions must be compactified on an even, self-dual lattice (a discrete subgroup of a linea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
String Theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interact with each other. On distance scales larger than the string scale, a string looks just like an ordinary particle, with its mass, charge, and other properties determined by the vibrational state of the string. In string theory, one of the many vibrational states of the string corresponds to the graviton, a quantum mechanical particle that carries the gravitational force. Thus, string theory is a theory of quantum gravity. String theory is a broad and varied subject that attempts to address a number of deep questions of fundamental physics. 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 conde ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anomaly (physics)
In quantum physics an anomaly or quantum anomaly is the failure of a symmetry of a theory's classical action to be a symmetry of any regularization of the full quantum theory. In classical physics, a classical anomaly is the failure of a symmetry to be restored in the limit in which the symmetry-breaking parameter goes to zero. Perhaps the first known anomaly was the dissipative anomaly in turbulence: time-reversibility remains broken (and energy dissipation rate finite) at the limit of vanishing viscosity. In quantum theory, the first anomaly discovered was the Adler–Bell–Jackiw anomaly, wherein the axial vector current is conserved as a classical symmetry of electrodynamics, but is broken by the quantized theory. The relationship of this anomaly to the Atiyah–Singer index theorem was one of the celebrated achievements of the theory. Technically, an anomalous symmetry in a quantum theory is a symmetry of the action, but not of the measure, and so not of the partition fu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
M-theory
M-theory is a theory in physics that unifies all consistent versions of superstring theory. Edward Witten first conjectured the existence of such a theory at a string theory conference at the University of Southern California in 1995. Witten's announcement initiated a flurry of research activity known as the second superstring revolution. Prior to Witten's announcement, string theorists had identified five versions of superstring theory. Although these theories initially appeared to be very different, work by many physicists showed that the theories were related in intricate and nontrivial ways. Physicists found that apparently distinct theories could be unified by mathematical transformations called S-duality and T-duality. Witten's conjecture was based in part on the existence of these dualities and in part on the relationship of the string theories to a field theory called eleven-dimensional supergravity. Although a complete formulation of M-theory is not known, such a formu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
T-duality
In theoretical physics, T-duality (short for target-space duality) is an equivalence of two physical theories, which may be either quantum field theories or string theories. In the simplest example of this relationship, one of the theories describes strings propagating in a spacetime shaped like a circle of some radius R, while the other theory describes strings propagating on a spacetime shaped like a circle of radius proportional to 1/R. The idea of T-duality was first noted by Bala Sathiapalan in an obscure paper in 1987. The two T-dual theories are equivalent in the sense that all observable quantities in one description are identified with quantities in the dual description. For example, momentum in one description takes discrete values and is equal to the number of times the string winds around the circle in the dual description. The idea of T-duality can be extended to more complicated theories, including superstring theories. The existence of these dualities implies that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
S-duality
In theoretical physics, S-duality (short for strong–weak duality, or Sen duality) is an equivalence of two physical theories, which may be either quantum field theories or string theories. S-duality is useful for doing calculations in theoretical physics because it relates a theory in which calculations are difficult to a theory in which they are easier. In quantum field theory, S-duality generalizes a well established fact from classical electrodynamics, namely the invariance of Maxwell's equations under the interchange of electric and magnetic fields. One of the earliest known examples of S-duality in quantum field theory is Montonen–Olive duality which relates two versions of a quantum field theory called ''N'' = 4 supersymmetric Yang–Mills theory. Recent work of Anton Kapustin and Edward Witten suggests that Montonen–Olive duality is closely related to a research program in mathematics called the geometric Langlands program. Another realization of S-duality in quan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Open String (physics)
Open or OPEN may refer to: Music * Open (band), Australian pop/rock band * The Open (band), English indie rock band * ''Open'' (Blues Image album), 1969 * ''Open'' (Gotthard album), 1999 * ''Open'' (Cowboy Junkies album), 2001 * ''Open'' (YFriday album), 2001 * ''Open'' (Shaznay Lewis album), 2004 * ''Open'' (Jon Anderson EP), 2011 * ''Open'' (Stick Men album), 2012 * ''Open'' (The Necks album), 2013 * ''Open'', a 1967 album by Julie Driscoll, Brian Auger and the Trinity * ''Open'', a 1979 album by Steve Hillage * "Open" (Queensrÿche song) * "Open" (Mýa song) * "Open", the first song on The Cure album ''Wish'' Literature * ''Open'' (Mexican magazine), a lifestyle Mexican publication * ''Open'' (Indian magazine), an Indian weekly English language magazine featuring current affairs * ''OPEN'' (North Dakota magazine), an out-of-print magazine that was printed in the Fargo, North Dakota area of the U.S. * Open: An Autobiography, Andre Agassi's 2009 memoir Computin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type I String Theory
In theoretical physics, type I string theory is one of five consistent supersymmetric string theories in ten dimensions. It is the only one whose strings are unoriented (both orientations of a string are equivalent) and the only one which contains not only closed strings, but also open strings. Overview The classic 1976 work of Ferdinando Gliozzi, Joël Scherk and David Olive paved the way to a systematic understanding of the rules behind string spectra in cases where only closed strings are present via modular invariance. It did not lead to similar progress for models with open strings, despite the fact that the original discussion was based on the type I string theory. As first proposed by Augusto Sagnotti in 1988, the type I string theory can be obtained as an orientifold of type IIB string theory, with 32 half-D9-branes added in the vacuum to cancel various anomalies giving it a gauge group of SO(32) via Chan-Paton factors. At low energies, type I string theory is desc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
String Duality
String or strings may refer to: *String (structure), a long flexible structure made from threads twisted together, which is used to tie, bind, or hang other objects Arts, entertainment, and media Films * ''Strings'' (1991 film), a Canadian animated short * ''Strings'' (2004 film), a film directed by Anders Rønnow Klarlund * ''Strings'' (2011 film), an American dramatic thriller film * ''Strings'' (2012 film), a British film by Rob Savage * ''Bravetown'' (2015 film), an American drama film originally titled ''Strings'' * ''The String'' (2009), a French film Music Instruments * String (music), the flexible element that produces vibrations and sound in string instruments * String instrument, a musical instrument that produces sound through vibrating strings ** List of string instruments * String piano, a pianistic extended technique in which sound is produced by direct manipulation of the strings, rather than striking the piano's keys Types of groups * String band, musical ens ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boundary Conditions
In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions. Boundary value problems arise in several branches of physics as any physical differential equation will have them. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems. A large class of important boundary value problems are the Sturm–Liouville problems. The analysis of these problems involves the eigenfunctions of a differential operator. To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input. Much theoretical work in the field of partial differential equ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
String (physics)
In physics, a string is a physical entity postulated in string theory and related subjects. Unlike elementary particles, which are zero-dimensional or point-like by definition, strings are one-dimensional extended entities. Researchers often have an interest in string theories because theories in which the fundamental entities are strings rather than point particles automatically have many properties that some physicists expect to hold in a fundamental theory of physics. Most notably, a theory of strings that evolve and interact according to the rules of quantum mechanics will automatically describe quantum gravity. Overview In string theory, the strings may be open (forming a segment with two endpoints) or closed (forming a loop like a circle) and may have other special properties. Prior to 1995, there were five known versions of string theory incorporating the idea of supersymmetry, which differed in the type of strings and in other aspects. Today these different string theor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Closed String
In physics, a string is a physical entity postulated in string theory and related subjects. Unlike elementary particles, which are zero-dimensional or point-like by definition, strings are one-dimensional extended entities. Researchers often have an interest in string theories because theories in which the fundamental entities are strings rather than point particles automatically have many properties that some physicists expect to hold in a fundamental theory of physics. Most notably, a theory of strings that evolve and interact according to the rules of quantum mechanics will automatically describe quantum gravity. Overview In string theory, the strings may be open (forming a segment with two endpoints) or closed (forming a loop like a circle) and may have other special properties. Prior to 1995, there were five known versions of string theory incorporating the idea of supersymmetry, which differed in the type of strings and in other aspects. Today these different string theor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Supergravity
In theoretical physics, supergravity (supergravity theory; SUGRA for short) is a modern field theory that combines the principles of supersymmetry and general relativity; this is in contrast to non-gravitational supersymmetric theories such as the Minimal Supersymmetric Standard Model. Supergravity is the gauge theory of local supersymmetry. Since the supersymmetry (SUSY) generators form together with the Poincaré algebra a superalgebra, called the super-Poincaré algebra, supersymmetry as a gauge theory makes gravity arise in a natural way. Gravitons Like any field theory of gravity, a supergravity theory contains a spin-2 field whose quantum is the graviton. Supersymmetry requires the graviton field to have a superpartner. This field has spin 3/2 and its quantum is the gravitino. The number of gravitino fields is equal to the number of supersymmetries. History Gauge supersymmetry The first theory of local supersymmetry was proposed by Dick Arnowitt and Pran Nath in 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
