Wilson loop

E860358

concept in gauge theory concept in quantum field theory gauge-invariant observable loop operator non-local observable

A Wilson loop is a gauge-invariant observable in gauge theories, defined by the path-ordered exponential of the gauge field around a closed loop, and is central to studying confinement and non-perturbative aspects of Yang–Mills theory.

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All labels observed (3)

Label	Occurrences
Wilson loop canonical	2
lightlike Wilson loop	1
supersymmetric Wilson loop	1

How this entity was disambiguated

This entity first appeared as the object of triple T10376361 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Wilson loop
Context triple: [Yang–Mills theory, relatedToConcept, Wilson loop]

A. Polyakov loop
The Polyakov loop is a gauge-invariant observable in finite-temperature quantum chromodynamics used to probe confinement and deconfinement phases of quarks and gluons.
B. Polyakov action
The Polyakov action is a fundamental formulation of string theory that describes the dynamics of relativistic strings via a two-dimensional worldsheet embedded in spacetime.
C. ’t Hooft coupling
The ’t Hooft coupling is a rescaled gauge coupling constant, central in large-N gauge theory and string theory, that remains finite in the ’t Hooft large-N limit and controls the strength of interactions.
D. Nambu–Goto action
The Nambu–Goto action is a fundamental formulation in string theory that describes the dynamics of relativistic strings by minimizing the area of their worldsheet in spacetime.
E. Montonen–Olive duality
Montonen–Olive duality is a conjectured symmetry in certain gauge theories, especially N=4 supersymmetric Yang–Mills, that exchanges electrically charged particles with magnetic monopoles and relates strong coupling to weak coupling.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Wilson loop
Target entity description: A Wilson loop is a gauge-invariant observable in gauge theories, defined by the path-ordered exponential of the gauge field around a closed loop, and is central to studying confinement and non-perturbative aspects of Yang–Mills theory.

A. Polyakov loop
The Polyakov loop is a gauge-invariant observable in finite-temperature quantum chromodynamics used to probe confinement and deconfinement phases of quarks and gluons.
B. Polyakov action
The Polyakov action is a fundamental formulation of string theory that describes the dynamics of relativistic strings via a two-dimensional worldsheet embedded in spacetime.
C. ’t Hooft coupling
The ’t Hooft coupling is a rescaled gauge coupling constant, central in large-N gauge theory and string theory, that remains finite in the ’t Hooft large-N limit and controls the strength of interactions.
D. Nambu–Goto action
The Nambu–Goto action is a fundamental formulation in string theory that describes the dynamics of relativistic strings by minimizing the area of their worldsheet in spacetime.
E. Montonen–Olive duality
Montonen–Olive duality is a conjectured symmetry in certain gauge theories, especially N=4 supersymmetric Yang–Mills, that exchanges electrically charged particles with magnetic monopoles and relates strong coupling to weak coupling.
F. None of above. chosen

Statements (50)

Predicate	Object
instanceOf	concept in gauge theory ⓘ concept in quantum field theory ⓘ gauge-invariant observable ⓘ loop operator ⓘ non-local observable ⓘ
actsOn	representation space of the gauge group ⓘ
consideredIn	N=4 supersymmetric Yang–Mills theory ⓘ supersymmetric gauge theories ⓘ
definedAs	path-ordered exponential of the gauge field around a closed loop ⓘ
definedInTermsOf	coupling constant g ⓘ gauge field A_μ ⓘ path ordering operator ⓘ representation of the gauge group ⓘ
dependsOn	choice of closed contour in spacetime ⓘ gauge connection ⓘ
hasExpectationValueBehavior	area law in confining phases ⓘ perimeter law in deconfined or Coulomb phases ⓘ
hasProperty	gauge invariance ⓘ non-locality ⓘ non-perturbative sensitivity ⓘ path dependence ⓘ
hasVariant	cusped Wilson loop ⓘ lightlike Wilson loop ⓘ linked to: Wilson loop supersymmetric Wilson loop ⓘ linked to: Wilson loop
mathematicallyFormulatedAs	trace of the holonomy of the gauge connection around a closed loop ⓘ
namedAfter	Kenneth G. Wilson ⓘ linked to: Kenneth Wilson
playsRoleIn	Makeenko–Migdal loop equations ⓘ loop equations in gauge theory ⓘ order parameters for confinement ⓘ strong coupling expansions on the lattice ⓘ
relatedTo	Polyakov loop ⓘ Wilson line ⓘ area law ⓘ holonomy ⓘ non-Abelian Stokes theorem ⓘ parallel transport ⓘ perimeter law ⓘ scattering amplitudes in planar N=4 SYM ⓘ ’t Hooft loop ⓘ
usedIn	AdS/CFT correspondence ⓘ Yang–Mills theory ⓘ lattice gauge theory ⓘ non-Abelian gauge theory ⓘ quantum chromodynamics ⓘ topological quantum field theory ⓘ
usedToStudy	color confinement ⓘ non-perturbative dynamics of gauge fields ⓘ phase structure of gauge theories ⓘ quark–antiquark potential ⓘ string–gauge duality ⓘ

How these facts were elicited

Referenced by (4)

Full triples — surface form annotated when it differs from this entity's canonical label.

Yang–Mills theory → relatedToConcept → Wilson loop ⓘ

Aharonov–Bohm effect → isRelatedTo → Wilson loop ⓘ

Wilson loop → hasVariant → supersymmetric Wilson loop ⓘ

linked to: Wilson loop

Wilson loop → hasVariant → lightlike Wilson loop ⓘ