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Unobservable spacetime curves needed to describe Dirac monopoles
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
Hypothetical particle with one magnetic pole
phases around the Dirac string are trivial, which means that the Dirac string must be unphysical. In other words, the Dirac string is merely an artifact
Magnetic_monopole
Mathematic demonstration of rotations in 3-dimensions
mathematics and physics, the plate trick, also known as Dirac's string trick (after Paul Dirac, who introduced and popularized it), the belt trick, or
Plate_trick
Maurice Dirac. Dirac large numbers hypothesis Dirac monopole Dirac string Dirac's string trick Dirac–Born–Infeld action Dirac path integral Dirac coordinates
List of things named after Paul Dirac
List_of_things_named_after_Paul_Dirac
Generalized function whose value is zero everywhere except at zero
In mathematical analysis, the Dirac delta function (or δ {\displaystyle {\boldsymbol {\delta }}} distribution), also known as the unit impulse, is a generalized
Dirac_delta_function
British physicist (1902–1984)
Paul Adrien Maurice Dirac (/dɪˈræk/ dih-RAK; 8 August 1902 – 20 October 1984) was an English theoretical physicist who was one of the founders of quantum
Paul_Dirac
Relativistic quantum mechanical wave equation
In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including
Dirac_equation
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
Electromagnetic quantum-mechanical effect in regions of zero magnetic and electric field
expressed as a Dirac string of infinitesimal diameter that contains the equivalent of all of the 4πg flux from a monopole "charge" g. The Dirac string starts
Aharonov–Bohm_effect
Principle in theoretical physics
The holographic principle is a property of string theories and a supposed property of quantum gravity that states that the description of a volume of space
Holographic_principle
Prize awarded by the International Centre for Theoretical Physics
The Dirac Medal of the ICTP is given each year by the International Centre for Theoretical Physics (ICTP) in honour of physicist Paul Dirac. The award
Dirac_Medal_(ICTP)
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)
Yang–Mills–Higgs magnetic monopole
Hooft–Polyakov monopole is a topological soliton similar to the Dirac monopole but without the Dirac string. It arises in the case of a Yang–Mills theory with a
't_Hooft–Polyakov_monopole
Indian physicist (born 1956)
Physics Prize, 2012, for his work on string theory Padma Bhushan in 2013 M.P. Birla Memorial Award in 2013 Dirac Medal in 2014 Oskar Klein Memorial Lecture
Ashoke_Sen
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 of subatomic structure
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called
String_theory
Riemannian manifold with SU(n) holonomy
so-called string theory landscape. Connected with each hole in the Calabi–Yau space is a group of low-energy string vibrational patterns. Since string theory
Calabi–Yau_manifold
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)
bound Exceptional Lie groups G2, F4, E6, E7, E8 ADE classification Dirac string P-form electrodynamics Mina Aganagić Daniele Amati Amir Amini Husam Qutteina
List_of_string_theory_topics
The history of string theory spans several decades of intense research including two superstring revolutions. Through the combined efforts of many researchers
History_of_string_theory
In physics and geometry: conjectured relation between pairs of Calabi–Yau manifolds
geometrically but are nevertheless equivalent when employed as extra dimensions of string theory. Early cases of mirror symmetry were discovered by physicists. Mathematicians
Mirror symmetry (string theory)
Mirror_symmetry_(string_theory)
Theory of strings with supersymmetry
is a shorthand for supersymmetric string theory because unlike bosonic string theory, it is the version of string theory that accounts for both fermions
Superstring_theory
Hypothetical elementary particle that mediates gravity
by Soviet physicists Dmitry Blokhintsev and Fyodor Galperin [ru]. Paul Dirac reintroduced the term in a number of lectures in 1959, noting that the energy
Graviton
Chinese-American physicist (1922–2025)
monopole, a type of magnetic monopole. Unlike the Dirac monopole, it has no singular Dirac string. Their 1975 paper, known as the Wu–Yang dictionary
Yang_Chen-Ning
Physics concept of subatomic structure
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
Heterotic_string_theory
Secondary characteristic classes of 3-manifolds
bound Exceptional Lie groups (G2, F4, E6, E7, E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification
Chern–Simons_form
Equivalence of two physical theories
examples of S-duality in string theory. The existence of these string dualities implies that seemingly different formulations of string theory are actually
S-duality
Duality between theories of gravity on anti-de Sitter space and conformal field theories
(AdS) that are used in theories of quantum gravity, formulated in terms of string theory or M-theory. On the other side of the correspondence are conformal
AdS/CFT_correspondence
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
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
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
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
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
52-dimensional exceptional simple Lie group
bound Exceptional Lie groups (G2, F4, E6, E7, E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification
F4_(mathematics)
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
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
Solitons in Euclidean spacetime
Archived 2015-04-02 at the Wayback Machine. He showed that zero modes of the Dirac equation in the instanton background lead to a non-perturbative multi-fermion
Instanton
American theoretical physicist (born 1940)
idea of the string theory landscape in 2003. Susskind was awarded the 1998 J. J. Sakurai Prize, the 2018 Oskar Klein Medal, and the Dirac Medal of the
Leonard_Susskind
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)
248-dimensional exceptional simple Lie group
physics and especially in string theory and supergravity. E8×E8 is the gauge group of one of the two types of heterotic string and is one of two anomaly-free
E8_(mathematics)
Peruvian theoretical physicist (b. 1954)
Barton Zwiebach Cantor (born October 4, 1954) is a Peruvian string theorist and professor at the Massachusetts Institute of Technology. Zwiebach was born
Barton_Zwiebach
Self-reinforcing single wave packet
solitons include the screw dislocation in a crystalline lattice, the Dirac string and the magnetic monopole in electromagnetism, the Skyrmion and the Wess–Zumino–Witten
Soliton
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
Framework of superstring theory
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
M-theory
Extended objects found in string theory
another object that arises under string T-duality). A 1989 paper by Leigh showed that D-brane dynamics are governed by the Dirac–Born–Infeld action. D-instantons
D-brane
Type of smooth complex surface of kodaira dimension 0
properties in detail. The type IIA string, the type IIB string, the E8×E8 heterotic string, the Spin(32)/Z2 heterotic string, and M-theory are related by compactification
K3_surface
Type of Riemannian manifold
bound Exceptional Lie groups (G2, F4, E6, E7, E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification
Hyperkähler_manifold
Manifold with Riemannian, complex and symplectic structure
bound Exceptional Lie groups (G2, F4, E6, E7, E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification
Kähler_manifold
Branch of string theory
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
F-theory
Simple Lie group; the automorphism group of the octonions
bound Exceptional Lie groups (G2, F4, E6, E7, E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification
G2_(mathematics)
Equivalence of two physical theories
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
T-duality
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
Unified field theory
the dimension of the total space must be 2 mod 8, and the G-index of the Dirac operator of the compact space must be nonzero. The above development generalizes
Kaluza–Klein_theory
Eight-dimensional Riemannian manifold
bound Exceptional Lie groups (G2, F4, E6, E7, E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification
Spin(7)-manifold
Lie algebra, usually infinite-dimensional
bound Exceptional Lie groups (G2, F4, E6, E7, E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification
Kac–Moody_algebra
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
Aspect of theoretical physics
physics, type II string theory is a unified term that includes both type IIA strings and type IIB strings theories. Type II string theory accounts for
Type_II_string_theory
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)
Topics referred to by the same term
hypertrophy pyloric stenosis Cosmic string, a hypothetical 1-dimensional (spatially) topological defect in various fields Dirac string, a fictitious one-dimensional
String_(disambiguation)
field theory Theories whose matter content consists only of spinor fields Dirac theory: free spinor field theory Thirring model Nambu–Jona-Lasinio model
List of quantum field theories
List_of_quantum_field_theories
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
78-dimensional exceptional simple Lie group
bound Exceptional Lie groups (G2, F4, E6, E7, E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification
E6_(mathematics)
Algebraic structure used in theoretical physics
bound Exceptional Lie groups (G2, F4, E6, E7, E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification
Supergroup_(physics)
Symmetry between bosons and fermions
statistics, and fermions, which have a half-integer-valued spin and follow Fermi–Dirac statistics. The names of bosonic partners of fermions are prefixed with
Supersymmetry
Generalized manifold
Orbifolding is therefore a general procedure of string theory to derive a new string theory from an old string theory in which the elements of G have been
Orbifold
Hypothetical physical concept
theory of relativity explained how they are connected. By the 1930s, Paul Dirac combined relativity and quantum mechanics and, working with other physicists
Theory_of_everything
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
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
Breakdown of conformal symmetry at the quantum level
quantum mechanics alone. String theory is not classically scale invariant since it is defined with a massive "string constant". In string theory, conformal symmetry
Conformal_anomaly
Special way of connecting two objects through flexible links
earliest published mention is “On a string problem of Dirac” by M.H.A. Newman, J. London Math. Soc., vol. 17 (1942). Dirac called it the “scissors puzzle”
Anti-twister_mechanism
Modern theory of gravitation that combines supersymmetry and general relativity
obligatory gauge symmetry in type I and heterotic string theories, and obtained in type II string theory by compactification on certain Calabi–Yau manifolds
Supergravity
Strong-weak duality in supersymmetric theories of theoretical physics
{\displaystyle \mathbf {E} } and B {\displaystyle \mathbf {B} } ? In 1931 Paul Dirac was studying the quantum mechanics of an electric charge moving in a magnetic
Montonen–Olive_duality
Recoil force on accelerating charged particle
the relativistic version is called the Lorentz–Dirac force or collectively known as Abraham–Lorentz–Dirac force. The equations are in the domain of classical
Abraham–Lorentz_force
Type of Lie algebra of interest in physics
bound Exceptional Lie groups (G2, F4, E6, E7, E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification
Loop_algebra
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
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
Model of a charged membrane
birth of string theory by almost a decade, he was the first to introduce what is now called a type of Nambu–Goto action for membranes. In the Dirac membrane
Dirac_membrane
Invariant action in bosonic string theory
Dirac membrane Nambu, Yoichiro, Lectures on the Copenhagen Summer Symposium (1970), unpublished. Zwiebach, Barton (2003). A First Course in String Theory
Nambu–Goto_action
Mathematics professorship in the University of Cambridge, England
others, Isaac Newton, Charles Babbage, George Stokes, Joseph Larmor, Paul Dirac and Stephen Hawking. Henry Lucas, in his will, bequeathed his library of
Lucasian Professor of Mathematics
Lucasian_Professor_of_Mathematics
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
Argentine physicist (born 1968)
Academy of Arts and Sciences, elected 2007 Dannie Heineman Prize, 2007 Dirac Medal of the ICTP, 2008 Pomeranchuk Prize, 2012 Breakthrough Prize in Fundamental
Juan_Maldacena
Type of geometry in mathematics
bound Exceptional Lie groups (G2, F4, E6, E7, E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification
Ricci-flat_manifold
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
longer gauge invariant and so also needs to be defined patchwise with the Dirac string off of a given patch interpreted itself as a D-brane. This extra complication
Ramond–Ramond_field
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
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
Hypothetical particle
Although string theory naturally incorporates Kaluza–Klein theory that first introduced the dilaton, perturbative string theories such as type I string theory
Dilaton
Base space for supersymmetric theories
bound Exceptional Lie groups (G2, F4, E6, E7, E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification
Superspace
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
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
British physicist
boundary conditions in string theory which have led to the postulation of D-branes and instantons. Green has been awarded the Paul Dirac and Maxwell Medals
Michael_Green_(physicist)
Generalization of electrodynamics
conventions do exist. The Kalb–Ramond field is an example with p = 2 in string theory; the Ramond–Ramond fields whose charged sources are D-branes are
P-form_electrodynamics
Theoretical framework in physics
Louis de Broglie, Werner Heisenberg, Max Born, Erwin Schrödinger, Paul Dirac, and Wolfgang Pauli. In the same year as his paper on the photoelectric
Quantum_field_theory
Generalization of a manifold
In mathematics and string theory, a conifold is a generalization of a manifold. Unlike manifolds, conifolds can contain conical singularities, i.e. points
Conifold
{\displaystyle I} yields heterotic E 8 × E 8 {\displaystyle E_{8}\times E_{8}} string theory and compactified over the one-dimensional sphere S 1 {\displaystyle
Hořava–Witten_theory
Application of K-theory in string theory
In string theory, K-theory classification refers to a conjectured application of K-theory (in abstract algebra and algebraic topology) to superstrings
K-theory_(physics)
Lower energy limit in string theory
corresponding to stable, non-perturbative states in both field theory and string theory. Their existence and properties are deeply connected to the underlying
Bogomol'nyi–Prasad–Sommerfield bound
Bogomol'nyi–Prasad–Sommerfield_bound
American particle physicist and string theorist
(/ɡroʊs/; born February 19, 1941) is an American theoretical physicist and string theorist. He shared the 2004 Nobel Prize in Physics with Frank Wilczek and
David_Gross
is the study of Dirac operators, and Dirac type operators in analysis and geometry, together with their applications. Examples of Dirac type operators
Clifford_analysis
Italian theoretical physicist
College Dublin, 2009 Felice Pietro Chisesi and Caterina Tomassoni Prize, 2009 Dirac Medal by ICTP, 2014 Honorary doctorate, Swansea University, 2015 Friedel-Volterra
Gabriele_Veneziano
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