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Theory of subatomic structure
Two theories related by a duality need not be string theories. For example, Montonen–Olive duality is an example of an S-duality relationship between quantum
String_theory
Class of symmetries in string theory
String duality is a class of symmetries in physics that link different string theories, theories which assume that the fundamental building blocks of
String_duality
Equivalence of two physical theories
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
S-duality
Physics concept of subatomic structure
I string theory — a theory that also contains open strings; this relation is called S-duality. The HO and HE theories are also related by T-duality. Because
Heterotic_string_theory
Equivalence of two physical theories
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
T-duality
Conjectured duality combining S-duality and T-duality
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
U-duality
unified, as long hoped, by new equivalences. These are known as S-duality, T-duality, U-duality, mirror symmetry, and conifold transitions. The different theories
History_of_string_theory
In physics and geometry: conjectured relation between pairs of Calabi–Yau manifolds
Other dualities that arise in string theory are S-duality, T-duality, and the AdS/CFT correspondence. For an accessible introduction to string theory
Mirror symmetry (string theory)
Mirror_symmetry_(string_theory)
Framework of superstring theory
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
M-theory
Duality between theories of gravity on anti-de Sitter space and conformal field theories
field theories. Much of the usefulness of the duality results from the fact that it is a strong–weak duality: when the fields of the quantum field theory
AdS/CFT_correspondence
Topics referred to by the same term
of dualities § Physics Mirror symmetry (string theory) Montonen–Olive duality Mysterious duality String duality, a class of symmetries S-duality T-duality
Duality
formalism String theory landscape History of string theory First superstring revolution Second superstring revolution T-duality S-duality U-duality Montonen–Olive
List_of_string_theory_topics
Principle in theoretical physics
sometimes called Maldacena duality named after the Argentinian physicist Juan Maldacena (after ref.) or gauge/gravity duality, is a conjectured relationship
Holographic_principle
Strong-weak duality in supersymmetric theories of theoretical physics
Montonen–Olive duality or electric–magnetic duality is the oldest known example of strong–weak duality or S-duality according to current terminology. It
Montonen–Olive_duality
Aspect of theoretical physics
realized that type IIA string theory is related to type IIB string theory by T-duality. Superstring theory Type I string Heterotic string Green, M.B.; Schwarz
Type_II_string_theory
Type of smooth complex surface of kodaira dimension 0
Severi (1909). Aspinwall, Paul (1996), "K3 surfaces and string duality", Fields, strings and duality (Boulder, CO, 1996), World Scientific, pp. 421–540,
K3_surface
Theory of strings with supersymmetry
take form of a G2 manifold. A particular exact symmetry of string/M-theory called T-duality (which exchanges momentum modes for winding number and sends
Superstring_theory
Hypothetical physical entity
In physics, a string is a physical entity postulated in string theory and related subjects. Unlike elementary particles, which are zero-dimensional or
String_(physics)
Isbell duality Jónsson–Tarski duality Lagrange duality Langlands dual Lefschetz duality Local Tate duality Opposite category Poincaré duality Twisted
List_of_dualities
Quantum description of black holes
particular variant of superstring theory called Type IIB (see also String duality), which holds that strings are both "open" (double-ended entities) and
Fuzzball_(string_theory)
Set of equations that describe superstring theory in a non-perturbative framework
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
Matrix_string_theory
Collection of possible string theory vacua
In string theory, the string theory landscape (or landscape of vacua) is the collection of possible false vacua, together comprising a collective "landscape"
String_theory_landscape
Theory in theoretical physics
and so arrive at the same geometry as in the dual theory. The mirror dual of this duality is another duality, which relates open strings in the B model
Topological_string_theory
Aspect of theoretical physics
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
Type_I_string_theory
Fretted string instrument optimized for richer sounds
twelve-string guitar is a steel-string guitar with 12 strings in six courses, which produces a thicker, more ringing tone than a standard six-string guitar
Twelve-string_guitar
Symmetry between bosons and fermions
realistic theories. A prime example of this has been the demonstration of S-duality in four-dimensional gauge theories that interchanges particles and monopoles
Supersymmetry
Process in particle physics
of twisted closed string tachyons, and by Simeon Hellerman and Ian Swanson, in a wider array of cases. The fate of the closed string tachyon in the 26-dimensional
Tachyon_condensation
American theoretical physicist and professor (born 1970)
low energy supersymmetric string compactifications (see KKLT mechanism). He made notable contributions to string theory duality (with Cumrun Vafa), the
Shamit_Kachru
Hypothetical elementary particle that mediates gravity
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
Graviton
Modern theory of gravitation that combines supersymmetry and general relativity
were related by "string dualities", some of which relate weak string-coupling - perturbative - physics in one model with strong string-coupling - non-perturbative
Supergravity
Extended objects found in string theory
holographic and M-theory dualities. The equations of motion of string theory require that the endpoints of an open string (a string with endpoints) satisfy
D-brane
Riemannian manifold with SU(n) holonomy
Bibcode:2004math.....10260C Greene, Brian (1997), String theory on Calabi–Yau manifolds, Fields, strings and duality (Boulder, CO, 1996), River Edge, NJ: World
Calabi–Yau_manifold
Hypothetical faster-than-light particle
of a tachyonic field is the tachyon of bosonic string theory. Tachyons are predicted by bosonic string theory and also the Neveu-Schwarz (NS) and NS-NS
Tachyon
Model in string theory
a dual resonance model arose during the early investigation (1968–1973) of string theory as an S-matrix theory of the strong interaction. The dual resonance
Dual_resonance_model
Hypothetical physical concept
mathematics and in ordinary, strongly-coupled gauge theory due to the Gauge/String duality. In the late 1990s, it was noted that one major hurdle in this endeavor
Theory_of_everything
248-dimensional exceptional simple Lie group
can be coupled to the N = 1 supergravity in ten dimensions. E8 is the U-duality group of supergravity on an eight-torus (in its split form). One way to
E8_(mathematics)
Unobservable spacetime curves needed to describe Dirac monopoles
In physics, a Dirac string is a one-dimensional curve in space, conceived of by the physicist Paul Dirac, stretching between two hypothetical Dirac monopoles
Dirac_string
Mathematical concept
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
Worldsheet
Theories in particle physics and cosmology
refers to several theories in particle physics and cosmology related to string theory, superstring theory and M-theory. The central idea is that the visible
Brane_cosmology
26-dimensional string theory
Bosonic string theory is the original version of string theory, developed in the late 1960s. It is so called because it contains only bosons in the spectrum
Bosonic_string_theory
Solitons in Euclidean spacetime
calculated by Nathan Seiberg and Edward Witten in "Electric – magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang–Mills
Instanton
Spanier–Whitehead duality is a duality theory in homotopy theory, based on a geometrical idea that a topological space X may be considered as dual to its complement
Spanier–Whitehead_duality
133-dimensional exceptional simple Lie group
SU(8). In string theory, E7 appears as a part of the gauge group of one of the (unstable and non-supersymmetric) versions of the heterotic string. It can
E7_(mathematics)
Duality in string theory
Gopakumar–Vafa duality is a duality in string theory, hence a correspondence between two different theories, in this case between Chern–Simons theory and
Gopakumar–Vafa_duality
Generalized manifold
inversion. The study of Calabi–Yau manifolds in string theory and the duality between different models of string theory (type IIA and IIB) led to the idea of
Orbifold
Branch of string theory
superstring theory in 10 dimensions. The SL(2,Z) S-duality symmetry of the resulting type IIB string theory is manifest because it arises as the group
F-theory
Type of Riemannian manifold
anti-self dual Yang–Mills equations: instanton moduli spaces, monopole moduli spaces, spaces of solutions to Nigel Hitchin's self-duality equations on
Hyperkähler_manifold
Extended physical object in string theory
Look up brane in Wiktionary, the free dictionary. In string theory and related theories (such as supergravity), a brane is a physical object that generalizes
Brane
Seven-dimensional Riemannian manifold
diffeomorphism types of new examples. These manifolds are important in string theory. They break the original supersymmetry to 1/8 of the original amount
G2_manifold
dual resonance model An early precursor of string theory. duality A hidden connection between two different theories, such as S-duality, T-duality, U-duality
Glossary_of_string_theory
Peruvian theoretical physicist (b. 1954)
Barton Zwiebach (born Barton Zwiebach Cantor, October 4, 1954) is a Peruvian string theorist and professor at the Massachusetts Institute of Technology. Zwiebach
Barton_Zwiebach
2019 art project by Ilya Khrzhanovsky
from loop quantum gravity by Carlo Rovelli Integral Equation for CFT/string duality by A.A.Migdal Darboux coordinates, Yang-Yang functional, and gauge theory
DAU_(project)
Formalism in string theory
String field theory (SFT) is a formalism in string theory in which the dynamics of relativistic strings is reformulated in the language of quantum field
String_field_theory
78-dimensional exceptional simple Lie group
27-dimensional, and a basis is given by the 27 lines on a cubic surface. The dual representation, which is inequivalent, is also 27-dimensional. In particle
E6_(mathematics)
Unified field theory
supported by experiments, but is a precursor to supergravity and modern string theory (in eleven-dimensional spacetime). In his 1921 article, Kaluza established
Kaluza–Klein_theory
Manifold with Riemannian, complex and symplectic structure
{\displaystyle H^{p,q}\cong {\overline {H^{n-p,n-q}}}} . It also follows from Serre duality. A simple consequence of Hodge theory is that every odd Betti number b
Kähler_manifold
Superstring quantization approach
"Supersymmetrical Dual String Theory," Nucl. Phys. B181 (1981), 502–530. M. B. Green, J. H. Schwarz, J. H., "Supersymmetrical Dual String Theory (II): Vertices
GS_formalism
International science award since 2012
2012). "Biggest science prize takes web tycoon from social networks to string theory". The Guardian. Archived from the original on May 1, 2022. Retrieved
Breakthrough Prize in Fundamental Physics
Breakthrough_Prize_in_Fundamental_Physics
Geometric space whose points represent algebro-geometric objects of some fixed kind
expectation values of a set of scalar fields, or to the moduli space of possible string backgrounds. Moduli spaces also appear in physics in topological field theory
Moduli_space
Low energy theories not compatible with string theory
always emerges. An example of this is T-duality, where there are two dual descriptions to understand a string theory with an internal geometry of a circle
Swampland_(physics)
Type of 2D conformal field theory
)} has been used by Juan Maldacena and Hirosi Ooguri to describe bosonic string theory on the three-dimensional anti-de Sitter space A d S 3 {\displaystyle
Wess–Zumino–Witten_model
Candidate "Theory of Everything"
In the 1980s, a new mathematical model of theoretical physics, called string theory, emerged. It showed how all the different subatomic particles known
Introduction_to_M-theory
Concept in general relativity and quantum field theory
entropy of a supersymmetric black hole in string theory, using methods based on D-branes and string duality. Their calculation was followed by many similar
Black_hole_thermodynamics
Superconformal Yang–Mills theory
Langlands dual group. This theory is also important in the context of the holographic principle. There is a duality between Type IIB string theory on
N = 4 supersymmetric Yang–Mills theory
N_=_4_supersymmetric_Yang–Mills_theory
Class of quantum field theory models
{\sqrt {\det g}}{\mathcal {D}}\Sigma .} This model proved to be relevant in string theory where the two-dimensional manifold is named worldsheet. Appreciation
Non-linear_sigma_model
Type of geometry in mathematics
Matrix string theory Non-critical string theory Non-linear sigma model Tachyon condensation RNS formalism GS formalism String duality T-duality S-duality U-duality
Ricci-flat_manifold
German physicist (born 1977)
ansatz), Beisert, Staudacher, and colleagues made progress in gauge/string duality for the case of supersymmetric gauge field theories with maximal symmetry
Niklas_Beisert
Mathematics concept
phenomenon called mirror symmetry first observed by physicists studying string theory. In an address to the 1994 International Congress of Mathematicians
Homological_mirror_symmetry
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
N_=_2_superstring
Speculative feature of the early universe
D-strings which are related to the F-strings by weak-strong or so called S-duality, or higher-dimensional D-, NS- or M-branes that are partially wrapped on
Cosmic_string
Lie algebra, usually infinite-dimensional
i } i = 1 n {\displaystyle \{\alpha _{i}\}_{i=1}^{n}} is a subset of the dual space h ∗ {\displaystyle {\mathfrak {h}}^{*}} satisfying the following three
Kac–Moody_algebra
Quantum mechanical model based on mathematical matrices
considered the worldvolume theory of a large number of D0-branes in Type IIA string theory. In geometry, it is often useful to introduce coordinates. For example
Matrix_theory_(physics)
Algebraic structure used in theoretical physics
Grozman, P.; Leites, D.; Shchepochkina, I. (2005). "Lie Superalgebras of String Theories". Acta Mathematica Vietnamica. 26 (2005): 27–63. arXiv:hep-th/9702120
Lie_superalgebra
Simple Lie group; the automorphism group of the octonions
ISSN 0002-9904, MR 0125155 Vogan, David A. Jr. (1994), "The unitary dual of G2", Inventiones Mathematicae, 116 (1): 677–791, Bibcode:1994InMat.116
G2_(mathematics)
Object in six-dimensional spacetime
supergravity solutions of Lunin and Mathur. David Tong (2002). "NS5-Branes, T-Duality and Worldsheet Instantons". Journal of High Energy Physics. 2002 (7): 013
NS5-brane
Asymmetry of classical and quantum action
doi:10.1103/PhysRevD.41.715. PMID 10012386. Conlon, Joseph (2016-08-19). Why String Theory? (1 ed.). CRC Press. p. 81. doi:10.1201/9781315272368. ISBN 978-1-315-27236-8
Anomaly_(physics)
Technique used to determine mass of hadrons
(AdS) inspired by the AdS/CFT correspondence (gauge/gravity duality) proposed for string theory. This procedure makes it possible to find analytic solutions
Light_front_holography
2D conformal field theory used in string theory
two-dimensional conformal field theory describing the worldsheet of a string in string theory. It was introduced by Stanley Deser and Bruno Zumino and independently
Polyakov_action
Algebra used in 2D conformal field theories and string theory
that plays an important role in two-dimensional conformal field theory and string theory. In addition to physical applications, vertex operator algebras have
Vertex_operator_algebra
Mathematical conjecture
submanifolds. On the other hand, T-duality does the same transformation in this case, thus "mirror symmetry is T-duality". The initial proposal of the SYZ
SYZ_conjecture
Hypothetical particle dual to the photon
theoretical physics, the dual photon is a hypothetical elementary particle that is a dual of the photon under electric–magnetic duality which is predicted by
Dual_photon
MR 2409679 Liu, Kefeng (2006), "Localization and conjectures from string duality", in Ge, Mo-Lin; Zhang, Weiping (eds.), Differential geometry and physics
Hodge_bundle
Generalization of a black hole to higher dimensions
spatial dimensions. That type of solution would be called a black p-brane. In string theory, the term black brane describes a group of D1-branes that are surrounded
Black_brane
Technique in theoretical physics
such as the mysterious duality. A flux compactification is a particular way to deal with additional dimensions required by string theory. It assumes that
Compactification_(physics)
52-dimensional exceptional simple Lie group
48 root vectors of F4 can be found as the vertices of the 24-cell in two dual configurations, representing the vertices of a disphenoidal 288-cell if the
F4_(mathematics)
Compact astronomical body
holes without singularities. For example, the fuzzball model, based on string theory, states that black holes are actually made up of quantum microstates
Black_hole
Application of K-theory in string theory
ten-dimensional spacetime, then a complication arises due to the self-duality of the RR fluxes. The duality uses the Hodge star, which depends on the metric and so
K-theory_(physics)
Hypothetical particle found in supergravity
physics, the dual graviton is a hypothetical elementary particle that is a dual of the graviton under electric–magnetic duality, as an S-duality, predicted
Dual_graviton
Delimited series of characters that represent a string in code
A string literal or anonymous string is a literal for a string value in source code. Commonly, a programming language includes a string literal code construct
String_literal
Eight-dimensional Riemannian manifold
Matrix string theory Non-critical string theory Non-linear sigma model Tachyon condensation RNS formalism GS formalism String duality T-duality S-duality U-duality
Spin(7)-manifold
Algebraic structure used in theoretical physics
properties of the supergroup. There is another related Hopf algebra which is the dual of the previous Hopf algebra. It can be identified with the Hopf algebra
Supergroup_(physics)
In string theory, an S-brane is a hypothetical and controversial counterpart of the D-brane, which is localized in time. Depending on the context the "S"
S-brane
American theoretical physicist
1951) is an American theoretical physicist known for his contributions to string theory, topological quantum field theory, general relativity and various
Edward_Witten
Secondary characteristic classes of 3-manifolds
Matrix string theory Non-critical string theory Non-linear sigma model Tachyon condensation RNS formalism GS formalism String duality T-duality S-duality U-duality
Chern–Simons_form
Russian theoretical physicist
Wilson's Nobel Prize-winning work. He formulated pioneering ideas in gauge/string duality long before the breakthrough of AdS/CFT using D-branes. Other insightful
Alexander Polyakov (physicist)
Alexander_Polyakov_(physicist)
British theoretical physicist (1937–2012)
contributions to string theory and duality theory, he is particularly known for his work on the GSO projection and Montonen–Olive duality. He was professor
David_Olive
Field theory linked to string theory
that capture the T-duality property of string theory as a manifest symmetry of a field theory. In double field theory, the T-duality transformation of
Double_field_theory
Brane in eleven-dimensional supergravity
M2-brane, is a spatially extended mathematical object (brane) that appears in string theory and in related theories (e.g. M-theory, F-theory). In particular
M2-brane
Two-form field
In theoretical physics in general and string theory in particular, the Kalb–Ramond field (named after Michael Kalb and Pierre Ramond), also known as the
Kalb–Ramond_field
field is constrained to satisfy the self-duality condition G5 = *G5 where * is the Hodge star. The self-duality condition cannot be imposed by a Lagrangian
Ramond–Ramond_field
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