Wess–Zumino–Witten model

E853118

conformal field theory exactly solvable model in quantum field theory sigma model two-dimensional quantum field theory

The Wess–Zumino–Witten model is a two-dimensional conformal field theory describing interacting scalar fields valued in a Lie group, notable for its topological Wess–Zumino term and applications in string theory and condensed matter physics.

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Observed surface forms (2)

Surface form	Occurrences
Wess–Zumino–Witten conformal field theory	1
Wess–Zumino–Witten term	1

Statements (48)

Predicate	Object
instanceOf	conformal field theory ⓘ exactly solvable model in quantum field theory ⓘ sigma model ⓘ two-dimensional quantum field theory ⓘ
admits	primary fields labeled by representations of affine Kac–Moody algebra ⓘ
centralChargeDependsOn	group and level ⓘ
describedBy	nonlinear sigma model action with Wess–Zumino term ⓘ
developedBy	Bruno Zumino NERFINISHED ⓘ Edward Witten NERFINISHED ⓘ Julius Wess NERFINISHED ⓘ
fieldContent	scalar fields valued in a Lie group ⓘ
hasApplication	construction of rational conformal field theories ⓘ description of edge states in topological phases ⓘ effective field theories for low-energy excitations ⓘ
hasCorrelationFunctions	constrained by Ward identities of current algebra ⓘ
hasParameter	level k ⓘ
hasProperty	exactly conformal ⓘ integrable in many cases ⓘ renormalizable in two dimensions ⓘ unitary for positive integer level ⓘ
hasSymmetry	affine Kac–Moody symmetry ⓘ chiral symmetry ⓘ conformal symmetry ⓘ current algebra symmetry ⓘ
hasTerm	Wess–Zumino term NERFINISHED ⓘ topological term ⓘ
hasTopologicalFeature	action defined modulo 2π times an integer ⓘ
namedAfter	Bruno Zumino NERFINISHED ⓘ Edward Witten NERFINISHED ⓘ Julius Wess NERFINISHED ⓘ
quantizesTo	discrete allowed levels from topological term ⓘ
relatedTo	Chern–Simons theory NERFINISHED ⓘ bosonization ⓘ current algebra representations ⓘ modular invariance in conformal field theory ⓘ nonlinear sigma model NERFINISHED ⓘ
spacetimeDimension	2 ⓘ
targetSpace	Lie group manifold ⓘ
usedIn	WZW models on AdS3 backgrounds ⓘ condensed matter physics ⓘ critical phenomena in one spatial dimension ⓘ quantum Hall effect ⓘ quantum spin chains ⓘ string theory ⓘ worldsheet description of strings on group manifolds ⓘ
usesMathematicalStructure	Lie algebra ⓘ Lie group ⓘ affine Kac–Moody algebra ⓘ

Referenced by (3)

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

Chern–Simons theory → quantizationLeadsTo → Wess–Zumino–Witten model ⓘ

Chern–Simons theory → boundaryTheory → Wess–Zumino–Witten model ⓘ

this entity surface form: Wess–Zumino–Witten conformal field theory

’t Hooft anomaly → relatesTo → Wess–Zumino–Witten model ⓘ

subject surface form: 't Hooft anomaly

this entity surface form: Wess–Zumino–Witten term