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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
2D conformal field theory used in string theory
an action of the two-dimensional conformal field theory describing the worldsheet of a string in string theory. It was introduced by Stanley Deser and Bruno
Polyakov_action
26-dimensional string theory
the string means that only interaction corresponding to an orientable worldsheet are allowed (e.g., two strings can only merge with equal orientation)
Bosonic_string_theory
Hypothetical physical entity
through spacetime, a string sweeps out a two-dimensional surface called its worldsheet. This is analogous to the one-dimensional worldline traced out by a point
String_(physics)
Superstring consistency requirement
of possible vertex operators in the worldsheet conformal field theory (CFT)—usually those with specific worldsheet fermion number and periodicity conditions
GSO_projection
Set of mathematical concepts in quantum gravity
which includes quantum corrections to the metric tensor, such as the worldsheet instantons. For example, the quantum volume of a cycle is computed from
Quantum_geometry
Compact astronomical body
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Black_hole
Formalism in string theory
closed strings. In addition, depending on the method used to fix the worldsheet diffeomorphisms and conformal transformations in the original free string
String_field_theory
Superstring quantization approach
(RNS) formalism is an approach to formulating superstrings in which the worldsheet has explicit superconformal invariance but spacetime supersymmetry is
RNS_formalism
Aspect of theoretical physics
dimensions. Both theories are based on oriented closed strings. On the worldsheet, they differ only in the choice of GSO projection. They were first discovered
Type_II_string_theory
Theory of subatomic structure
Interaction in the quantum world: worldlines of point-like particles or a worldsheet swept up by closed strings in string theory
String_theory
American theoretical physicist (born 1940)
principle Matrix theory (physics) String theory String theory landscape Worldsheet RST model Susskind–Glogower operator Kogut–Susskind fermions Fischler–Susskind
Leonard_Susskind
Class of quantum field theory models
relevant in string theory where the two-dimensional manifold is named worldsheet. Appreciation of its generalized renormalizability was provided by Daniel
Non-linear_sigma_model
Riemannian manifold with SU(n) holonomy
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Calabi–Yau_manifold
Hypothetical faster-than-light particle
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Tachyon
Compare and contrast article
to the worldsheet curvature of other strings, so their abundance through space-time determines the measure by which an average string worldsheet will be
Relationship between string theory and quantum field theory
Relationship_between_string_theory_and_quantum_field_theory
Principle in theoretical physics
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Holographic_principle
Indian physicist
David, Justin R.; Gopakumar, Rajesh (17 January 2007). "From spacetime to worldsheet: Four point correlators". Journal of High Energy Physics. 0701:063 (1):
Rajesh_Gopakumar
Branch of mathematics
manifolds, and these spaces find uses in string theory. In particular, worldsheets of strings are modelled by Riemann surfaces, and superstring theory predicts
Geometry
Dimensionality of space at which the character of the phase transition changes
be determined by the required cancellation of conformal anomaly on the worldsheet; it is 26 for the bosonic string theory and 10 for superstring theory
Critical_dimension
Supersymmetric extension to the Virasoro algebra
periodicity depends on the choice of coordinates on the worldsheet. In the w-frame, in which the worldsheet of a single string state is described as a long cylinder
Super_Virasoro_algebra
Geometric space whose points represent algebro-geometric objects of some fixed kind
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Moduli_space
Generalization of a black hole to higher dimensions
metric with signature (−, +, +, +, ...), σ are the coordinates for the worldsheet of the black p-brane, u is its four-velocity, r is the radial coordinate
Black_brane
Theory in theoretical physics
Topological string theory is obtained by a topological twist of the worldsheet description of ordinary string theory: the operators are given different
Topological_string_theory
Theory in physics
interactions between quarks. In order for a string theory to be consistent, the worldsheet theory must be conformally invariant. The obstruction to conformal symmetry
Non-critical_string_theory
Hypothetical elementary particle that mediates gravity
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Graviton
Convex polytope of parenthesizations
"Scattering Forms and the Positive Geometry of Kinematics, Color and the Worldsheet", Journal of High Energy Physics, 2018: 96, arXiv:1711.09102, doi:10
Associahedron
Duality between theories of gravity on anti-de Sitter space and conformal field theories
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
AdS/CFT_correspondence
Hypothetical particle
Berman & Perry (2006).) In string theory, there is also a dilaton in the worldsheet CFT – two-dimensional conformal field theory. The exponential of its vacuum
Dilaton
Israeli American theoretical physicist
Dine, Seiberg, X. G. Wen, and Witten studied instantons on the string worldsheet. Gregory Moore and Seiberg studied Rational Conformal Field Theories.
Nathan_Seiberg
Concept in string theory
string travels through spacetime it traces out a surface, called the worldsheet of the string. Unfortunately, the moduli space of such parametrized surfaces
Gromov–Witten_invariant
Algebra describing 2D conformal symmetry
Virasoro algebra comprises the generators of the conformal group of the worldsheet, the stress tensor in string theory obeys the commutation relations of
Virasoro_algebra
Framework of superstring theory
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
M-theory
2D conformal field theories
such as minimal models. Moreover, they play an important role in the worldsheet approach to string theory. In a free bosonic CFT, the Virasoro algebra's
Massless free scalar bosons in two dimensions
Massless_free_scalar_bosons_in_two_dimensions
Symmetry between bosons and fermions
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Supersymmetry
Concept in physics
the object is a point particle) or worldsheets (if the object is larger than a point). The worldline or worldsheet only describes the motion of the object;
Postulates of special relativity
Postulates_of_special_relativity
Secondary characteristic classes of 3-manifolds
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Chern–Simons_form
Concept in theoretical physics
groups G 1 {\displaystyle G_{1}} and G 2 {\displaystyle G_{2}} and the worldsheet parity operator Ω p {\displaystyle \Omega _{p}} (such that Ω p : σ → 2
Orientifold
Theory of quantum gravity merging quantum mechanics and general relativity
geometry (gravitons) are both described as excitations on the string worldsheet. The background dependence of string theory can have physical consequences
Loop_quantum_gravity
Model of the extended complex plane plus a point at infinity
a relativistic model for the celestial sphere. In string theory, the worldsheets of strings are Riemann surfaces, and the Riemann sphere, being the simplest
Riemann_sphere
Invariant action in bosonic string theory
generate timelike diffeomorphisms and spacelike diffeomorphisms on the worldsheet. The Hamiltonian H = P ⋅ X ˙ − L = 0 {\displaystyle H=P\cdot {\dot {X}}-{\mathcal
Nambu–Goto_action
Topics referred to by the same term
action, two-dimensional action of a conformal field theory describing the worldsheet of a string in string theory 't Hooft–Polyakov monopole, a topological
Polyakov_(disambiguation)
248-dimensional exceptional simple Lie group
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
E8_(mathematics)
Argentine physicist (1940–2021)
infinite-dimensional Lie algebra which describes the conformal symmetry of the worldsheet of a string embedded in spacetime. A supersymmetric generalization of
Miguel Ángel Virasoro (physicist)
Miguel_Ángel_Virasoro_(physicist)
Collection of possible string theory vacua
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
String_theory_landscape
Theory proposed by Roger Penrose
S2CID 36625491. Adamo, Tim; Casali, Eduardo; Skinner, David (2015-02-01). "A worldsheet theory for supergravity". Journal of High Energy Physics. 2015 (2): 116
Twistor_theory
Modern theory of gravitation that combines supersymmetry and general relativity
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Supergravity
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
Type of Riemannian manifold
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Hyperkähler_manifold
Extended physical object in string theory
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Brane
Manifold with Riemannian, complex and symplectic structure
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Kähler_manifold
Unified field theory
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Kaluza–Klein_theory
Type of geometry in mathematics
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Ricci-flat_manifold
Breakdown of conformal symmetry at the quantum level
massive "string constant". In string theory, conformal symmetry on the worldsheet is a local Weyl symmetry. There is also a potential gravitational anomaly
Conformal_anomaly
Type of smooth complex surface of kodaira dimension 0
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
K3_surface
Simple Lie group; the automorphism group of the octonions
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
G2_(mathematics)
Theory of strings with supersymmetry
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Superstring_theory
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
History_of_string_theory
Japanese-American nobel-winning physicist
which describes the dynamics of a relativistic string as the area of the worldsheet swept out in spacetime. This formalism became a central component of modern
Yoichiro_Nambu
Solitons in Euclidean spacetime
lead to a mass for the photon. In 2-dimensional abelian gauge theories worldsheet instantons are magnetic vortices. They are responsible for many nonperturbative
Instanton
Process in particle physics
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Tachyon_condensation
Two-form field
while the Kalb–Ramond field must be integrated over the two-dimensional worldsheet of the string. In particular, while the action for a charged particle
Kalb–Ramond_field
South African theoretical physicist (1928-2016)
conformal invariance to calculate tree level string amplitudes on many worldsheet domains. Mandelstam was the first to explicitly construct the fermion
Stanley_Mandelstam
Mathematics concept
X. When the Riemann surfaces have empty boundary, they represent the worldsheets of closed strings. To cover the case of open strings, one must introduce
Homological_mirror_symmetry
Theories in particle physics and cosmology
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Brane_cosmology
Algebraic structure used in theoretical physics
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Lie_superalgebra
Extension to the Poincaré group
Yang–Mills theory due its relevance for AdS/CFT correspondence. Also, the worldsheet in string theory is described by a two-dimensional conformal field theory
Conformal_symmetry
Lie algebra, usually infinite-dimensional
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Kac–Moody_algebra
Path of an object through spacetime
World line, worldsheet, and world volume, as they are derived from particles, strings, and branes
World_line
Candidate "Theory of Everything"
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Introduction_to_M-theory
Equivalence of two physical theories
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
T-duality
Type of 2D conformal field theory
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Wess–Zumino–Witten_model
Equivalence of two physical theories
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
S-duality
model of string theory. It is a superstring theory in the sense that the worldsheet theory is supersymmetric. However, the spacetime spectrum is not supersymmetric
Type_0_string_theory
Field theory of a point particle confined to move on a fixed manifold
Euclidean space for condensed matter applications, or a Riemann surface, the worldsheet in string theory. The ∂ μ ϕ = ∂ ϕ / ∂ x μ {\displaystyle \partial _{\mu
Sigma_model
Special collection of states in closed string theory
conjugacy class of G, we have a different superselection sector (wrt the worldsheet). The conjugacy class consisting of the identity gives rise to the untwisted
Twisted_sector
Graphical representation of supersymmetric algebras
Hubsch, "On Dimensional Extension of Supersymmetry: From Worldlines to Worldsheets" Zhang, Yan X. (2011). "Adinkras for Mathematicians". arXiv:1111.6055
Adinkra_symbols_(physics)
78-dimensional exceptional simple Lie group
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
E6_(mathematics)
Extended objects found in string theory
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
D-brane
Branch of string theory
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
F-theory
Asymmetry of classical and quantum action
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Anomaly_(physics)
Eight-dimensional Riemannian manifold
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Spin(7)-manifold
Quantum mechanical model based on mathematical matrices
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Matrix_theory_(physics)
Peruvian theoretical physicist (b. 1954)
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Barton_Zwiebach
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Twisted_K-theory
In physics and geometry: conjectured relation between pairs of Calabi–Yau manifolds
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Mirror symmetry (string theory)
Mirror_symmetry_(string_theory)
Unobservable spacetime curves needed to describe Dirac monopoles
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Dirac_string
Seven-dimensional Riemannian manifold
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
G2_manifold
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
List of quantum field theories
List_of_quantum_field_theories
Type of Kac–Moody algebras
coset models. As a consequence, affine Lie algebras also appear in the worldsheet description of string theory. The Heisenberg algebra defined by generators
Affine_Lie_algebra
Algebra used in 2D conformal field theories and string theory
which transform 'like tensors' under coordinate transformations of the worldsheet in string theory. L ( z ) = ∑ L m z − m − 2 {\displaystyle L(z)=\sum L_{m}z^{-m-2}}
Vertex_operator_algebra
Generalized manifold
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Orbifold
Set of equations that describe superstring theory in a non-perturbative framework
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Matrix_string_theory
Object in six-dimensional spacetime
solutions of Lunin and Mathur. David Tong (2002). "NS5-Branes, T-Duality and Worldsheet Instantons". Journal of High Energy Physics. 2002 (7): 013. arXiv:hep-th/0204186
NS5-brane
Physics concept of subatomic structure
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Heterotic_string_theory
{\displaystyle p^{+}} is a constant and τ {\displaystyle \tau } is the worldsheet time. light cone coordinates The light cone gauge, Samir D. Mathur QCD
Light_cone_gauge
52-dimensional exceptional simple Lie group
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
F4_(mathematics)
Base space for supersymmetric theories
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Superspace
Generalization of a manifold
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Conifold
E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold
Ramond–Ramond_field
WORLDSHEET
WORLDSHEET
WORLDSHEET
WORLDSHEET
Male
African
son of Moi (the clan).
Boy/Male
German
Brave.
Girl/Female
Tamil
Somdatta | ஸோமà¯à®¤à®¾à®¤à¯à®¤à®¾Â
Moon, Religious drink
Boy/Male
Buddhist, Indian, Japanese
Open Heart / Mind
Boy/Male
Hindu, Indian, Sanskrit, Tamil
King of Dancers; Lord Shiva; King of the Art of Dancing
Girl/Female
Tamil
Dakshana | தகà¯à®·à®¾à®¨à®¾Â
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Telugu
Lord Shiva
Boy/Male
Hindu, Indian
Entire Knowledgeable
Boy/Male
American, Anglo, Australian, British, Chinese, Christian, English
Wide River-crossing
Girl/Female
Tamil
In flower, Bright as the dawn
WORLDSHEET
WORLDSHEET
WORLDSHEET
WORLDSHEET
WORLDSHEET