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string theory
String theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...
topics
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String theory
String theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...
Strings
String (physics)
A string is a hypothetical vibrating one-dimensional sub-atomic structure and one of the main objects of study in string theory, a branch of theoretical physics. There are different string theories, many of which are unified by M-theory. A string is an object with a one-dimensional spatial extent,...
Nambu-Goto action
Nambu-Goto action
The Nambu–Goto action is the simplest invariant action in bosonic string theory, and is also used in other theories that investigate string-like objects . It is the starting point of the analysis of zero-thickness string behavior, using the principles of Lagrangian mechanics...
Polyakov action
Polyakov action
In physics, the Polyakov action is the two-dimensional action of a conformal field theory describing the worldsheet of a string in string theory...
Bosonic string theory
Bosonic string theory
Bosonic string theory is the original version of string theory, developed in the late 1960s.In the early 1970s, supersymmetry was discovered in the context of string theory, and a new version of string theory called superstring theory became the real focus...
Superstring theory
Superstring theory
Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modelling them as vibrations of tiny supersymmetric strings...
Type I string
Type II string
Type IIA string theory
Type IIB string theory
Heterotic string
Heterotic string
In physics, a heterotic string is a peculiar mixture of the bosonic string and the superstring...
N=2 superstring
N=2 superstring
In string theory, N=2 superstring is a theory in which the worldsheet admits N=2 supersymmetry rather than N=1 supersymmetry as in the usual superstring. The target space is four dimensional, but either none or two of them are time-like, i.e. it has either 4+0 or 2+2 dimensions...
M-theory
M-theory
In theoretical physics, M-theory is an extension of string theory in which 11 dimensions are identified. Because the dimensionality exceeds that of superstring theories in 10 dimensions, proponents believe that the 11-dimensional theory unites all five string theories...
Matrix theory
Introduction to M-theory
Introduction to M-theory
In non-technical terms, M-theory presents an idea about the basic substance of the universe.-Background:In the early years of the 20th century, the atom – long believed to be the smallest building-block of matter – was proven to consist of even smaller components called protons, neutrons...
F-theory
F-theory
F-theory is a branch of string theory developed by Cumrun Vafa. The new vacua described as F-theory were discovered by Vafa, and it also allowed string theorists to construct new realistic vacua — in the form of F-theory compactified on elliptically fibered Calabi-Yau four-folds...
String field theory
String field theory
String field theory is a formalism in string theory in which the dynamics of relativistic strings is reformulated in the language of quantum field theory...
Matrix string theory
Matrix string theory
In 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 for a large value of N...
Nonlinear sigma model
Tachyon condensation
Tachyon condensation
In particle physics, theoretical processes that eliminate or resolve particles or fields into better understood phenomena are called, by extension and metaphor with the macroscopic process, "condensation"...
RNS formalism
RNS formalism
In theoretical physics, the RNS formalism or Ramond-Neveu-Schwarz formalism is a particular method to describe the degrees of freedom of a string in superstring theory in which the elementary fields on the worldsheet are the bosonic scalar fields describing the embedding of the string in spacetime,...
String theory landscape
String theory landscape
The string theory landscape or anthropic landscape refers to the large number of possible false vacua in string theory. The "landscape" includes so many possible configurations that some physicists think that the known laws of physics, the standard model and general relativity with a positive...
History of string theory
History of string theory
The history of string theory is probably more relevant to its core science than histories of other physical sciences. String theory is presently, and essentially, a non physically testable science, and thus arguably not Physics, yet its derivation parallels testable physics...
First superstring revolution
Second superstring revolution
String duality
String duality
String 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....
T-duality
T-duality
T-duality is a symmetry of quantum field theories with differing classical descriptions, of which the relationship between small and large distances in various string theories is a special case. Discussion of the subject originated in a paper by T. S. Buscher and was further developed by Martin...
S-duality
S-duality
In theoretical physics, S-duality is an equivalence of two quantum field theories or string theories. An S-duality transformation maps states and vacua with coupling constant g in one theory to states and vacua with coupling constant 1/g in the dual theory...
U-duality
U-duality
In physics, U-duality is a symmetry of string theory or M-theory combining S-duality and T-duality transformations. The term is most often met in the context of the "U-duality group" of M-theory as defined on a particular background space . This is the union of all the S- and T-dualities...
Montonen-Olive duality
Montonen-Olive duality
In theoretical physics, Montonen–Olive duality is the oldest known example of S-duality or a strong-weak duality. It generalizes the electro-magnetic symmetry of Maxwell's equations...
Mysterious duality
Particles and fields
Graviton
Graviton
In physics, the graviton is a hypothetical elementary particle that mediates the force of gravitation in the framework of quantum field theory. If it exists, the graviton must be massless and must have a spin of 2...
Dilaton
Dilaton
In particle physics, a dilaton is a hypothetical particle. It also appears in Kaluza-Klein theory's compactifications of extra dimensions when the volume of the compactified dimensions vary....
Tachyon
Tachyon
A tachyon is a hypothetical subatomic particle that always moves faster than light. In the language of special relativity, a tachyon would be a particle with space-like four-momentum and imaginary proper time. A tachyon would be constrained to the space-like portion of the energy-momentum graph...
Ramond-Ramond field
Ramond-Ramond field
In theoretical physics, Ramond–Ramond fields are differential form fields in the 10-dimensional spacetime of type II supergravity theories, which are the classical limits of type II string theory. The ranks of the fields depend on which type II theory is considered...
Kalb-Ramond field
Kalb-Ramond field
In theoretical physics in general and string theory in particular, the Kalb–Ramond field, also known as the NS-NS B-field, is a quantum field that transforms as a two-form i.e. an antisymmetric tensor field with two indices....
Magnetic monopole
Magnetic monopole
A magnetic monopole is a hypothetical particle in particle physics that is a magnet with only one magnetic pole . In more technical terms, a magnetic monopole would have a net "magnetic charge". Modern interest in the concept stems from particle theories, notably the grand unified and superstring...
Branes
D-brane
D-brane
In string theory, D-branes are a class of extended objects upon which open strings can end with Dirichlet boundary conditions, after which they are named. D-branes were discovered by Dai, Leigh and Polchinski, and independently by Hořava in 1989...
S-brane
S-brane
In string theory, an S-brane is a hypothetical and controversial counterpart of a D-brane, which, unlike a D-brane, is localized in time. Depending on the context the "S" stands for "Strominger", "Sen", or "Space-like". The S-brane was originally proposed by Andrew Strominger in his speculative...
Black brane
Black brane
In general relativity, a black brane is a solution of the equations that generalizes a black hole solution but it is also extended —and translationally symmetric— in p additional spatial dimensions...
Black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...
s
Black string
Black string
A black string is a higher dimensional generalization of a black hole in which the event horizon is topologically equivalent to S2 × S1 and spacetime is asymptotically Md−1 × S1....
Brane cosmology
Brane cosmology
Brane cosmology refers to several theories in particle physics and cosmology motivated by, but not exclusively derived from, superstring theory and M-theory.-Brane and bulk:...
Quiver diagram
Quiver diagram
In physics, a quiver diagram is a graph representing the matter content of a gauge theory that describes D-branes on orbifolds.Each node of the graph corresponds to a factor U of the gauge group, and each link represents a field in the bifundamental representation.The relevance of quiver diagrams...
Hanany-Witten transition
Hanany-Witten transition
In 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...
Supersymmetry
Supersymmetry
In particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...
Supergravity
Supergravity
In theoretical physics, supergravity is a field theory that combines the principles of supersymmetry and general relativity. Together, these imply that, in supergravity, the supersymmetry is a local symmetry...
Superspace
Superspace
"Superspace" has had two meanings in physics. The word was first used by John Wheeler to describe the configuration space of general relativity; for example, this usage may be seen in his famous 1973 textbook Gravitation....
Lie superalgebra
Lie superalgebra
In mathematics, a Lie superalgebra is a generalisation of a Lie algebra to include a Z2-grading. Lie superalgebras are important in theoretical physics where they are used to describe the mathematics of supersymmetry...
Lie supergroup
Conformal field theory
Conformal field theory
A conformal field theory is a quantum field theory that is invariant under conformal transformations...
Virasoro algebra
Virasoro algebra
In mathematics, the Virasoro algebra is a complex Lie algebra, given as a central extension of the complex polynomial vector fields on the circle, and is widely used in conformal field theory and string theory....
Mirror symmetry
Mirror symmetry
In physics and mathematics, mirror symmetry is a relation that can exist between two Calabi-Yau manifolds. It happens, usually for two such six-dimensional manifolds, that the shapes may look very different geometrically, but nevertheless they are equivalent if they are employed as hidden...
Conformal anomaly
Conformal anomaly
Conformal anomaly is an anomaly i.e. a quantum phenomenon that breaks the conformal symmetry of the classical theory.A classically conformal theory is a theory which, when placed on a surface with arbitrary background metric, has an action that is invariant under rescalings of the background metric...
Conformal algebra
Superconformal algebra
Superconformal algebra
In theoretical physics, the superconformal algebra is a graded Lie algebra or superalgebra that combines the conformal algebra and supersymmetry. It generates the superconformal group in some cases .In two dimensions, the superconformal algebra is infinite-dimensional...
Vertex operator algebra
Vertex operator algebra
In mathematics, a vertex operator algebra is an algebraic structure that plays an important role in conformal field theory and related areas of physics...
Loop algebra
Kac-Moody algebra
Wess-Zumino-Witten model
Wess-Zumino-Witten model
In theoretical physics and mathematics, the Wess–Zumino–Witten model, also called the Wess–Zumino–Novikov–Witten model, is a simple model of conformal field theory whose solutions are realized by affine Kac–Moody algebras...
Geometry
Kaluza-Klein theory
Compactification
Compactification (physics)
In physics, compactification means changing a theory with respect to one of its space-time dimensions. Instead of having a theory with this dimension being infinite, one changes the theory so that this dimension has a finite length, and may also be periodic....
Why 10 dimensions?
Kähler manifold
Kähler manifold
In mathematics, a Kähler manifold is a manifold with unitary structure satisfying an integrability condition.In particular, it is a Riemannian manifold, a complex manifold, and a symplectic manifold, with these three structures all mutually compatible.This threefold structure corresponds to the...
Ricci-flat manifold
Ricci-flat manifold
In mathematics, Ricci-flat manifolds are Riemannian manifolds whose Ricci curvature vanishes. In physics, they represent vacuum solutions to the analogues of Einstein's equations for Riemannian manifolds of any dimension, with vanishing cosmological constant...
Calabi-Yau manifold
Calabi-Yau manifold
A Calabi-Yau manifold is a special type of manifold that shows up in certain branches of mathematics such as algebraic geometry, as well as in theoretical physics...
HyperKähler manifold
Hyperkähler manifold
In differential geometry, a hyperkähler manifold is a Riemannian manifold of dimension 4k and holonomy group contained in Sp In differential geometry, a hyperkähler manifold is a Riemannian manifold of dimension 4k and holonomy group contained in Sp(k) In differential geometry, a hyperkähler...
K3 surface
K3 surface
In mathematics, a K3 surface is a complex or algebraic smooth minimal complete surface that is regular and has trivial canonical bundle.In the Enriques-Kodaira classification of surfaces they form one of the 5 classes of surfaces of Kodaira dimension 0....
G
_{2}
manifold
G2 manifold
In differential geometry, a G2 manifold is a seven-dimensional Riemannian manifold with holonomy group G2. The group G_2 is one of the five exceptional simple Lie groups...
Spin(7) manifold
Generalized complex manifold
Generalized complex structure
In the field of mathematics known as differential geometry, a generalized complex structure is a property of a differential manifold that includes as special cases a complex structure and a symplectic structure...
Orbifold
Orbifold
In the mathematical disciplines of topology, geometry, and geometric group theory, an orbifold is a generalization of a manifold...
Conifold
Conifold
In mathematics and string theory, a conifold is a generalization of a manifold. Unlike manifolds, conifolds can contain conical singularities i.e. points whose neighbourhoods look like cones over a certain base...
Orientifold
Orientifold
In theoretical physics orientifold is a generalization of the notion of orbifold, proposed by Augusto Sagnotti in 1987. The novelty is that in the case of string theory the non-trivial element of the orbifold group includes the reversal of the orientation of the string...
Moduli space
Moduli space
In algebraic geometry, a moduli space is a geometric space whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects...
Horava-Witten domain wall
Horava-Witten domain wall
In theoretical physics, a Hořava–Witten domain wall is a type of domain wall that behaves as a boundary of the eleven-dimensional spacetime in M-theory....
K-theory (physics)
K-theory (physics)
In string theory, the K-theory classification refers to a conjectured application of K-theory to superstrings, to classify the allowed Ramond-Ramond field strengths as well as the charges of stable D-branes....
Twisted K-theory
Twisted K-theory
In mathematics, twisted K-theory is a variation on K-theory, a mathematical theory from the 1950s that spans algebraic topology, abstract algebra and operator theory....
Gauge theory
Gauge theory
In physics, gauge invariance is the property of a field theory in which different configurations of the underlying fundamental but unobservable fields result in identical observable quantities. A theory with such a property is called a gauge theory...
Anomalies
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 an anomaly is the failure of a symmetry to be restored in the limit in which the symmetry-breaking...
Instanton
Instanton
An instanton is a notion appearing in theoretical and mathematical physics. Mathematically, a Yang–Mills instanton is a self-dual or anti-self-dual connection in a principal bundle over a four-dimensional Riemannian manifold that plays the role of physical space-time in non-abelian gauge theory...
s
Chern-Simons form
Chern-Simons form
In mathematics, the Chern–Simons forms are certain secondary characteristic classes. They have been found to be of interest in gauge theory, and they define the action of Chern–Simons theory...
Bogomol'nyi Prasad Sommerfield bound
Exceptional Lie groups
G
_{2}
,
F
_{4}
,
E
_{6}
,
E
_{7}
,
E
_{8}
E8 (mathematics)
In mathematics, E8 is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding root lattice, which has rank 8...
ADE classification
ADE classification
In mathematics, the ADE classification is the complete list of simply laced Dynkin diagrams or other mathematical objects satisfying analogous axioms; "simply laced" means that there are no multiple edges, which corresponds to all simple roots in the root system forming angles of \pi/2 = 90^\circ ...
Dirac string
Dirac string
In physics, a Dirac string is a fictitious one-dimensional curve in space, conceived of by the physicist Paul Dirac, stretching between two Dirac magnetic monopoles with opposite magnetic charges, or from one magnetic monopole out to infinity. The gauge potential cannot be defined on the Dirac...
P-form electrodynamics
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