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Thermal Wilson loop
In quantum field theory, the Polyakov loop is the thermal analogue of the Wilson loop, acting as an order parameter for confinement in pure gauge theories
Polyakov_loop
Russian theoretical physicist
Alexander Markovich Polyakov (Russian: Алекса́ндр Ма́ркович Поляко́в; born 27 September 1945) is a Russian-American theoretical physicist, formerly at
Alexander Polyakov (physicist)
Alexander_Polyakov_(physicist)
Gauge field loop operator
duals to Wilson loops, and Polyakov loops, which are the thermal version of Wilson loops. To properly define Wilson loops in gauge theory requires considering
Wilson_loop
Magnetic loop operator dual to the Wilson loop
't Hooft lines are determined by Λ w {\displaystyle \Lambda _{w}} . Polyakov loop 't Hooft, G. (1978). "On the phase transition towards permanent quark
't_Hooft_loop
Phenomenon in quantum chromodynamics
order operator for confinement are thermal versions of Wilson loops known as Polyakov loops. The confinement scale or QCD scale is the scale at which the
Color_confinement
Yang–Mills–Higgs magnetic monopole
In theoretical physics, the 't Hooft–Polyakov monopole is a topological soliton similar to the Dirac monopole but without the Dirac string. It arises in
't_Hooft–Polyakov_monopole
Quantum field theory at non-zero temperatures
as Umezawa formalism or thermo field dynamics. Matsubara summation Polyakov loop Quantum thermodynamics Quantum statistical mechanics Mustafa, Munshi
Thermal_quantum_field_theory
Nuclear physicist
1103/PhysRevD.73.014019. Rößner, S.; Ratti, C.; Weise, W. (8 February 2007). "Polyakov loop, diquarks, and the two-flavor phase diagram". Physical Review D. 75
Claudia_Ratti
Gauge symmetry cannot be spontaneously broken
are Wilson loops and their thermal equivalents, Polyakov loops. Another nonlocal operator that acts as a order operator is the 't Hooft loop. Since gauge
Elitzur's_theorem
D E F G H I J K L M N O P Q R S T U V W X Y Z 't Hooft loop 't Hooft symbol 't Hooft–Polyakov monopole (2+1)-dimensional topological gravity (n-p) reaction
Index of physics articles (!$@)
Index_of_physics_articles_(!$@)
Russian-American physicist (b. 1945)
work was subsequently developed by Migdal and Polyakov, working independently, into the Migdal–Polyakov conformal bootstrap, and was a precursor to the
Alexander_Migdal
Type of Lie algebra of interest in physics
In mathematics, loop algebras are certain types of Lie algebras, of particular interest in theoretical physics. For a Lie algebra g {\displaystyle {\mathfrak
Loop_algebra
2D conformal field theory used in string theory
In physics, the Polyakov action is an action of the two-dimensional conformal field theory describing the worldsheet of a string in string theory. It was
Polyakov_action
American mathematician
Knizhnik–Polyakov–Zamolodchikov (KPZ) relation for fractal scaling dimensions in Liouville quantum gravity. Sheffield also defined conformal loop ensembles
Scott_Sheffield
Breakdown of conformal symmetry at the quantum level
(equivalent to the Fredholm theory of a classical field theory). One-loop (N-loop) Feynman diagrams are proportional to ℏ {\displaystyle \hbar } ( ℏ N
Conformal_anomaly
Duality between theories of gravity on anti-de Sitter space and conformal field theories
on in two articles, one by Steven Gubser, Igor Klebanov and Alexander Polyakov, and another by Edward Witten. By 2015, Maldacena's article had over 10
AdS/CFT_correspondence
Functions that can't be described by perturbation theory
perturbation theory, at any finite order. In quantum field theory, 't Hooft–Polyakov monopoles, domain walls, flux tubes, and instantons are examples. A concrete
Non-perturbative
26-dimensional string theory
theory can be said to be defined by the path integral quantization of the Polyakov action: I 0 [ g , X ] = T 8 π ∫ M d 2 ξ g g m n ∂ m x μ ∂ n x ν G μ ν (
Bosonic_string_theory
This is a list of string theory topics. Strings Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string
List_of_string_theory_topics
Manifold with Riemannian, complex and symplectic structure
superstring revolution String theory landscape Theory Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string
Kähler_manifold
Surname list
theory terminology: 't Hooft matching condition 't Hooft loop 't Hooft symbol 't Hooft–Polyakov monopole Hooft at the Database of Surnames in The Netherlands
Hooft
Lower energy limit in string theory
gauge theories. Specifically, it was shown that the mass of a 't Hooft-Polyakov monopole and a Julia-Zee dyon is bounded from below by a quantity proportional
Bogomol'nyi–Prasad–Sommerfield bound
Bogomol'nyi–Prasad–Sommerfield_bound
Riemannian manifold with SU(n) holonomy
superstring revolution String theory landscape Theory Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string
Calabi–Yau_manifold
Mathematical concept
≤ σ < 2 π {\displaystyle 0\leq \sigma <2\pi } . In order to define the Polyakov action, the world-sheet is equipped with a world-sheet metric g {\displaystyle
Worldsheet
Class of quantum field theory models
Chiral model Little Higgs Skyrmion, a soliton in non-linear sigma models Polyakov action WZW model Fubini–Study metric, a metric often used with non-linear
Non-linear_sigma_model
Principle in theoretical physics
elaborated in articles by Steven Gubser, Igor Klebanov, and Alexander Markovich Polyakov, and by Edward Witten. By 2015, Maldacena's article had over 10,000 citations
Holographic_principle
Principle in quantum field theory
change by integrating out massive degrees of freedom. 't Hooft–Polyakov monopole 't Hooft loop 't Hooft symbol In the context of quantum field theory, "UV"
Anomaly_matching_condition
Framework of superstring theory
string theory, there is only one kind of string, which may look like a small loop or segment of ordinary string, and it can vibrate in different ways. On distance
M-theory
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
Extension of quantum field theory to curved spacetime
Thirring–Wess Toda Conformal 2D free massless scalar Liouville Logarithmic Minimal Polyakov Wess–Zumino–Witten Supersymmetric 4D N = 1 N = 1 super Yang–Mills Seiberg–Witten
Quantum field theory in curved spacetime
Quantum_field_theory_in_curved_spacetime
Secondary characteristic classes of 3-manifolds
superstring revolution String theory landscape Theory Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string
Chern–Simons_form
Dutch theoretical physicist
magnetic monopoles. These monopoles are called 't Hooft–Polyakov monopoles, after Alexander Polyakov, who obtained the same result independently. 't Hooft
Gerard_'t_Hooft
Seven-dimensional Riemannian manifold
superstring revolution String theory landscape Theory Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string
G2_manifold
theory known as string theory. These theories are without supersymmetry. Polyakov action Nambu-Goto action Bosonic string theory Kondo model (s-d model)
List of quantum field theories
List_of_quantum_field_theories
Computer programming language
Archived from the original (PDF) on 28 January 2022. Retrieved 5 April 2023. Polyakov, Konstantin. "Doklady na konferenciyah i seminarah [Reports at conferences
PascalABC.NET
Unobservable spacetime curves needed to describe Dirac monopoles
superstring revolution String theory landscape Theory Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string
Dirac_string
Two-form field
superstring revolution String theory landscape Theory Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string
Kalb–Ramond_field
Extended physical object in string theory
open (forming a segment with two endpoints) or closed (forming a closed loop). D-branes are an important class of branes that arise when one considers
Brane
Hypothetical particle with one magnetic pole
sophisticated theories, it is superseded by a smooth solution such as the 't Hooft–Polyakov monopole. A gauge theory like electromagnetism is defined by a gauge field
Magnetic_monopole
Compact astronomical body
microstates and need not have a singularity or an event horizon. The theory of loop quantum gravity proposes that the curvature and density at the centre of
Black_hole
Type of geometry in mathematics
superstring revolution String theory landscape Theory Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string
Ricci-flat_manifold
Theory with particles of spin more than two
of interest as models of AdS/CFT correspondence. In 2002, Klebanov and Polyakov put forward a conjecture that the free and critical O ( N ) {\displaystyle
Higher-spin_theory
Lie algebra, usually infinite-dimensional
superstring revolution String theory landscape Theory Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string
Kac–Moody_algebra
Concept in theoretical physics
superstring revolution String theory landscape Theory Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string
Orientifold
Generalization of a manifold
superstring revolution String theory landscape Theory Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string
Conifold
Theory of subatomic structure
elaborated in articles by Steven Gubser, Igor Klebanov, and Alexander Markovich Polyakov, and by Edward Witten. By 2010, Maldacena's article had over 7000 citations
String_theory
248-dimensional exceptional simple Lie group
superstring revolution String theory landscape Theory Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string
E8_(mathematics)
Candidate "Theory of Everything"
in a mathematically consistent way. In comparison, other theories such as loop quantum gravity are considered by physicists and researchers to be less elegant
Introduction_to_M-theory
Type of smooth complex surface of kodaira dimension 0
superstring revolution String theory landscape Theory Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string
K3_surface
Mathematical theorem about the real analytic Eisenstein series
)|^{4}} . This formula has been used in string theory for the one-loop computation in Polyakov's perturbative approach. The second Kronecker limit formula states
Kronecker_limit_formula
Theory in physics
ISBN 0-521-63303-6. Vol. 2: Superstring theory and beyond. ISBN 0-521-63304-4. Polyakov, A.M. (1981). "Quantum geometry of bosonic strings". Physics Letters B
Non-critical_string_theory
Collection of possible string theory vacua
"Counting flux vacua", JHEP 0401, 060 (2004). Baggott, Jim (2018). Quantum Space Loop Quantum Gravity and the Search for the Structure of Space, Time, and the
String_theory_landscape
Belgian-American theoretical physicist
amplitudes for the bosonic Polyakov string, Nucl. Phys. B, vol. 269, 1986, pp. 205–234 doi:10.1016/0550-3213(86)90372-X with Phong: Loop amplitudes for the fermionic
Eric_D'Hoker
133-dimensional exceptional simple Lie group
superstring revolution String theory landscape Theory Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string
E7_(mathematics)
Eight-dimensional Riemannian manifold
superstring revolution String theory landscape Theory Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string
Spin(7)-manifold
superstring revolution String theory landscape Theory Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string
Ramond–Ramond_field
American physicist (1931–2023)
He died in Pasadena, California on April 21, 2023, at the age of 92. Polyakov action Stanley Deser, John Simon Guggenheim Foundation Chang, Kenneth (May
Stanley_Deser
Hypothetical elementary particle that mediates gravity
semiclassical corrections such as one-loop diagrams behave normally. However, Feynman diagrams with at least two loops lead to ultraviolet divergences. These
Graviton
Type of Riemannian manifold
superstring revolution String theory landscape Theory Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string
Hyperkähler_manifold
Theories in particle physics and cosmology
been used to put weak limits on large extra dimensions. Kaluza–Klein theory Loop quantum cosmology "Session D9 - Experimental Tests of Short Range Gravitation"
Brane_cosmology
of bosonic string theory. String theory is formulated in terms of the Polyakov action, which describes how strings move through space and time. Like springs
History_of_string_theory
Process in particle physics
superstring revolution String theory landscape Theory Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string
Tachyon_condensation
Award
astronaut Thomas Patten Stafford Russian cosmonaut Valeri Vladimirovich Polyakov German astronaut Thomas Reiter American astronaut William Shepherd Canadian
Medal "For Merit in Space Exploration"
Medal_"For_Merit_in_Space_Exploration"
Simple Lie group; the automorphism group of the octonions
superstring revolution String theory landscape Theory Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string
G2_(mathematics)
Hypothetical faster-than-light particle
superstring revolution String theory landscape Theory Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string
Tachyon
Hypothetical physical entity
may be open (forming a segment with two endpoints) or closed (forming a loop like a circle) and may have other special properties. Prior to 1995, there
String_(physics)
Award
Anatoly Solovyev 1988 — Musa Manarov 1989 — Sergei Krikalev 1989 — Valeri Polyakov 1990 — Aleksandr Nikolayevich Balandin 1991 — Gennadi Manakov 1991 — Viktor
Pilot-Cosmonaut_of_the_USSR
critical systems was suggested by Alexander Belavin, Alexander Markovich Polyakov and Alexander Zamolodchikov in 1984, which eventually led to the development
History of quantum field theory
History_of_quantum_field_theory
Object in six-dimensional spacetime
Neveu Nielsen van Nieuwenhuizen Novikov Olive Ooguri Ovrut Polchinski Polyakov Rajaraman Ramond Randall Randjbar-Daemi Roček Rohm Sagnotti Scherk Schwarz
NS5-brane
Theoretical framework in physics
non-Abelian gauge theories. The 't Hooft–Polyakov monopole was discovered theoretically by 't Hooft and Alexander Polyakov, flux tubes by Holger Bech Nielsen
Quantum_field_theory
Theoretical process
superstring revolution String theory landscape Theory Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string
Hanany–Witten_transition
Definition of scientific term
PMID 9725825. Retrieved 2015-10-16. Sheval EV, Prusov AN, Kireev II, Fais D, Polyakov VY (2002). "Organization of higher-level chromatin structures (chromomere
Chromomere
Geometric space whose points represent algebro-geometric objects of some fixed kind
superstring revolution String theory landscape Theory Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string
Moduli_space
Set of equations that describe superstring theory in a non-perturbative framework
Neveu Nielsen van Nieuwenhuizen Novikov Olive Ooguri Ovrut Polchinski Polyakov Rajaraman Ramond Randall Randjbar-Daemi Roček Rohm Sagnotti Scherk Schwarz
Matrix_string_theory
78-dimensional exceptional simple Lie group
superstring revolution String theory landscape Theory Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string
E6_(mathematics)
Peruvian theoretical physicist (b. 1954)
superstring revolution String theory landscape Theory Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string
Barton_Zwiebach
Theory of rapid universe expansion
Sidney Coleman applied the instanton techniques developed by Alexander Polyakov and collaborators to study the fate of the false vacuum in quantum field
Cosmic_inflation
Moscow Metro station
names (Arbatskaya and Smolenskaya). Arbatskaya was designed by Leonid Polyakov, Valentin Pelevin and Yury Zenkevich. Since it was meant to serve as a
Arbatskaya (Arbatsko–Pokrovskaya line)
Arbatskaya_(Arbatsko–Pokrovskaya_line)
Mathematical theory
superstring revolution String theory landscape Theory Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string
Twisted_K-theory
Elementary particle involved with rest mass
ISBN 978-981-238-231-3, containing Higgs's story of the Higgs Boson. Migdal, A. A.; Polyakov, A. M. (1966). "Spontaneous Breakdown of Strong Interaction Symmetry and
Higgs_boson
superstring revolution String theory landscape Theory Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string
S-brane
Type of 2D conformal field theory
the existence of this symmetry is through repeated application of the Polyakov–Wiegmann identity regarding products of G {\displaystyle G} -valued fields:
Wess–Zumino–Witten_model
Superstring quantization approach
have no branch cuts. Secondly, the OPEs must also closed. Lastly, the one-loop amplitudes must be modular invariant. The GSO projection is the projection
RNS_formalism
Quantum mechanical model based on mathematical matrices
Neveu Nielsen van Nieuwenhuizen Novikov Olive Ooguri Ovrut Polchinski Polyakov Rajaraman Ramond Randall Randjbar-Daemi Roček Rohm Sagnotti Scherk Schwarz
Matrix_theory_(physics)
52-dimensional exceptional simple Lie group
superstring revolution String theory landscape Theory Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string
F4_(mathematics)
Solitons in Euclidean spacetime
't Hooft–Polyakov monopoles play the role of instantons. In his 1977 paper Quark Confinement and Topology of Gauge Groups, Alexander Polyakov demonstrated
Instanton
Modular space station in low Earth orbit
non-toxic, water coolant loop used to cool and dehumidify the atmosphere, which transfers collected heat into an external liquid ammonia loop. From the heat exchangers
International_Space_Station
Equivalence of two physical theories
Neveu Nielsen van Nieuwenhuizen Novikov Olive Ooguri Ovrut Polchinski Polyakov Rajaraman Ramond Randall Randjbar-Daemi Roček Rohm Sagnotti Scherk Schwarz
S-duality
Equivalence of two physical theories
Neveu Nielsen van Nieuwenhuizen Novikov Olive Ooguri Ovrut Polchinski Polyakov Rajaraman Ramond Randall Randjbar-Daemi Roček Rohm Sagnotti Scherk Schwarz
T-duality
In physics and geometry: conjectured relation between pairs of Calabi–Yau manifolds
one-dimensional objects called strings. These strings look like small segments or loops of ordinary string. String theory describes how strings propagate through
Mirror symmetry (string theory)
Mirror_symmetry_(string_theory)
Modern theory of gravitation that combines supersymmetry and general relativity
Neveu Nielsen van Nieuwenhuizen Novikov Olive Ooguri Ovrut Polchinski Polyakov Rajaraman Ramond Randall Randjbar-Daemi Roček Rohm Sagnotti Scherk Schwarz
Supergravity
Aspect of theoretical physics
Neveu Nielsen van Nieuwenhuizen Novikov Olive Ooguri Ovrut Polchinski Polyakov Rajaraman Ramond Randall Randjbar-Daemi Roček Rohm Sagnotti Scherk Schwarz
Type_II_string_theory
Formalism in string theory
D'Hoker, Eric; Giddings, Steven B. (1987). "Unitarity of the closed bosonic Polyakov string". Nuclear Physics B. 291. Elsevier BV: 90–112. Bibcode:1987NuPhB
String_field_theory
Mathematical model of ferromagnetism in statistical mechanics
representation in terms of non-interacting fermionic strings by Alexander Polyakov and Vladimir Dotsenko. This construction has been carried on the lattice
Ising_model
superstring revolution String theory landscape Theory Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string
Hořava–Witten_theory
Prize awarded by the International Centre for Theoretical Physics
particularly in theories of compact objects and cosmic evolution." 1986 Alexander Polyakov "being among the first to emphasize the importance of scale invariance
Dirac_Medal_(ICTP)
Extended objects found in string theory
two D-branes approach each other the interaction is captured by the one loop annulus amplitude of strings between the two branes. The scenario of two
D-brane
Property of a differential manifold that includes complex structures
superstring revolution String theory landscape Theory Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string
Generalized_complex_structure
Mathematical symbol used in algebras
different duality properties. Instanton 't Hooft anomaly 't Hooft–Polyakov monopole 't Hooft loop 't Hooft, G. (1976). "Computation of the quantum effects due
't_Hooft_symbol
Asymmetry of classical and quantum action
mean that a non-perturbative global anomaly cannot be captured by one loop or any loop perturbative Feynman diagram calculations—examples include the Witten
Anomaly_(physics)
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POLYAKOV LOOP
POLYAKOV LOOP
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