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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Wilson loop canonical | 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.
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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.
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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.
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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.
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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
NERFINISHED
ⓘ
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 NERFINISHED ⓘ supersymmetric Wilson loop NERFINISHED ⓘ |
| mathematicallyFormulatedAs | trace of the holonomy of the gauge connection around a closed loop ⓘ |
| namedAfter | Kenneth G. Wilson NERFINISHED ⓘ |
| playsRoleIn |
Makeenko–Migdal loop equations
NERFINISHED
ⓘ
loop equations in gauge theory ⓘ order parameters for confinement ⓘ strong coupling expansions on the lattice ⓘ |
| relatedTo |
Polyakov loop
ⓘ
Wilson line NERFINISHED ⓘ area law ⓘ holonomy ⓘ non-Abelian Stokes theorem NERFINISHED ⓘ parallel transport ⓘ perimeter law ⓘ scattering amplitudes in planar N=4 SYM ⓘ ’t Hooft loop ⓘ |
| usedIn |
AdS/CFT correspondence
NERFINISHED
ⓘ
Yang–Mills theory NERFINISHED ⓘ lattice gauge theory ⓘ non-Abelian gauge theory ⓘ quantum chromodynamics NERFINISHED ⓘ 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
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Wilson loop Description of subject: 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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.