String theory

physical theory of quantized one-dimensional objects with conformal symmetry, which can describe gravitation, gauge theory and other phenomena

In theories of quantum gravity, the graviton is the hypothetical elementary particle that mediates the force of gravitational interaction. It is a quantum of gravitational wave energy. There is no complete quantum field theory of gravitons due to the unsolved mathematical problem of renormalization in general relativity. This problem is avoided in string theory, which has the graviton as a massless state of a fundamental string, but that theory has not made sufficient progress.

A tachyon () or tachyonic particle is a hypothetical particle that always travels faster than light. Physicists posit that faster-than-light particles cannot exist because they are inconsistent with the known laws of physics. If such particles did exist they perhaps could be used to send signals faster than light and into the past. According to the theory of relativity this would violate causality, leading to logical paradoxes such as the grandfather paradox. Tachyons would exhibit the unusual property of increasing in speed as their energy decreases, and would require infinite energy to slow

In physics, M-theory is a theory 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 wa

theory of strings with supersymmetry

In string theory and related theories (such as supergravity), a brane is a physical object that generalizes the notion of a zero-dimensional point particle, a one-dimensional string, or a two-dimensional membrane to higher-dimensional objects. Branes are dynamical objects which can propagate through spacetime according to the rules of quantum mechanics. They have mass and can have other attributes such as charge.

field theory on a spacetime with small, compact extra dimensions beyond the large observed dimensions

Riemannian manifold with SU(n) holonomy

duality between theories of gravity on anti-de Sitter space and conformal field theories

cosmological model involving repetitions of Big Bangs followed by Big Crunches

hypothetical physical entity in string theory

conjectured relation between pairs of Calabi–Yau manifolds; situation where two Calabi–Yau manifolds look very different geometrically but are nevertheless equivalent when employed as extra dimensions of string theory

several theories in particle physics and cosmology related to superstring theory and M-theory

thumb|alt=D3-brane & D2-brane|D3-brane & D2-brane In string theory, D-branes, short for Dirichlet membrane, are a class of extended objects upon which open strings can end with Dirichlet boundary conditions, after which they are named. D-branes are typically classified by their spatial dimension, which is indicated by a number written after the D. A D0-brane is a single point, a D1-brane is a line (sometimes called a "D-string"), a D2-brane is a plane, and a D25-brane fills the highest-dimensional space considered in bosonic string theory. There are also instantonic D(−1)-branes, which are lo

26-dimensional string theory without supersymmetry, with a tachyon in its spectrum

In particle physics, the hypothetical dilaton is a particle of a scalar field \varphi that appears in theories with extra dimensions when the volume of the compactified dimensions varies. It appears as a radion in Kaluza–Klein theory's compactifications of extra dimensions. In Brans–Dicke theory of gravity, Newton's constant is not presumed to be constant but instead 1/G is replaced by a scalar field \varphi and the associated particle is the dilaton.

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 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

procedure of putting a physical field theory on a spacetime of the form K × Y, where K is a compact manifold

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.

10-dimensional string theory with N=2 supersymmetry (32 supercharges), either as N=(2,0) (type IIA) or N=(1,1) (type IIB)

superstring theory in which one of the left- and right-movers is supersymmetric and the other bosonic

summability method in physics

field of cosmology

theory of strings where left- and right-movers are identified via orientifolding, obtained as IIB string theory with 32 spacetime-filling D9-branes (producing a O(32) gauge group) and a spacetime-filling O9-plane

a type of smooth complex surface of Kodaira dimension 0

aspect of history

procedure of putting a quantum field theory on fewer spatial dimensions than before

proposed higher dimensions of space and time

space of vacua of string theory, or equivalently quantum field theories obtainable as low-energy limits of string theory

quantum description of black holes

process by which a system can lower its energy by spontaneously producing particles that fills the volume of the system

physics model in which particles (except the graviton) are localized on a 4d brane inside a 5d anti-de Sitter space

secondary characteristic class defined for odd-dimensional manifolds with G-bundles with connection; in 2n−1 dimensions, defined as (formal) exterior antiderivative of tr(Fⁿ) where F is the curvature of the connection

In string theory, a worldsheet is a two-dimensional manifold which describes the embedding of a string in spacetime. The term was coined by Leonard Susskind as a direct generalization of the world line concept for a point particle in special and general relativity.

a theory of strings in a second-quantized formalism on the target space (as opposed to the first-quantized formalism on the worldsheet)

nonlinear generalization of electrodynamics with a maximum field strength

Special product of manifolds

equivalence between the derived Fukaya category of a symplectic manifold and the derived category of coherent sheaves on a complex manifold

In string theory, the NS5-brane is a fundamental extended object in six-dimensional spacetime that carries magnetic charge under the Neveu–Schwarz B-field. The tension of the NS5-brane is inversely proportional to the Newton gravitational constant, making it a solitonic object of the theory. Coincident NS5-branes cannot be described by weakly coupled string theory, making them non-perturbative. When NS5-branes are separated on a circle transverse to their worldvolume, their description is given by a particular conformal field theory due to Giveon and Kutasov. When these fivebranes rotate on a

action describing the worldsheet of a string in string theory

non-technical introduction to M-theory, the leading contender for a universal "Theory of Everything" that unifies gravity with other forces such as electromagnetism.

action for string theory

invariant in symplectic topology and algebraic geometry

string theory with a topologically twisted 𝒩=(2,2) sigma-model action on the worldsheet and 6 target-space dimensions

In physics, U-duality (short for unified 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 (symmetry) group" of M-theory as defined on a particular background space (topological manifold). This is the union of all the S-duality and T-duality available in that topology. The narrow meaning of the word "U-duality" is one of those dualities that can be classified neither as an S-duality, nor as a T-duality - a transformation that exchanges a large geometry of one theory with the strong

In theoretical physics, F-theory is a branch of string theory developed by Iranian-American physicist Cumrun Vafa. The new vacua described by F-theory were discovered by Vafa and allowed string theorists to construct new realistic vacua — in the form of F-theory compactified on elliptically fibered Calabi–Yau four-folds. The letter "F" supposedly stands for "Father" in relation to "Mother"-theory.

expansion of the product of two local operators inserted close to each other as an asymptotic series with local-operator coefficients

class of symmetries in string theory

smooth map from a Riemann surface into an almost complex manifold that satisfies the Cauchy–Riemann equation

conjecture that gravity must be the weakest force

type of symmetry

quantum field theory

RNS formalism

string theory with worldsheet supersymmetry but no target-space supersymmetry

two-dimensional conformal field theory

mathematical conjecture

space of semiclassical field theories that cannot be consistently embedded in string theory

2-form gauge field in the NS–NS sector in 10-dimensional supergravity and superstring theory, under which fundamental strings are charged

Theory in physics

particular perturbative analysis of quantum field theories