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.
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 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.