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.

Try in SPARQL Jump to: Surface forms Disambiguation Statements Elicitation Referenced by

All labels observed (6)

Label	Occurrences
Wess–Zumino–Witten model canonical	3
Wess–Zumino–Witten models	2
Wess–Zumino term	1
Wess–Zumino–Witten conformal field theory	1
Wess–Zumino–Witten term	1
Wess–Zumino–Witten term in effective field theories	1

How this entity was disambiguated

This entity first appeared as the object of triple T10269840 — 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: Wess–Zumino–Witten model
Context triple: [Chern–Simons theory, quantizationLeadsTo, Wess–Zumino–Witten model]

A. Chern–Simons theory
Chern–Simons theory is a topological quantum field theory in three dimensions that plays a central role in modern geometry, topology, and theoretical physics, particularly in the study of knot invariants and gauge fields.
B. Rozansky–Witten theory
Rozansky–Witten theory is a three-dimensional topological quantum field theory associated with hyperkähler manifolds that yields invariants of 3-manifolds and links via holomorphic symplectic geometry.
C. Donaldson–Witten theory
Donaldson–Witten theory is a four-dimensional topological quantum field theory derived from twisting N=2 supersymmetric Yang–Mills theory, used to compute Donaldson invariants of smooth four-manifolds.
D. Witten index
The Witten index is a topological invariant in supersymmetric quantum field theory that counts the difference between bosonic and fermionic zero-energy states, providing insight into supersymmetry breaking.
E. Seiberg–Witten theory
Seiberg–Witten theory is a framework in quantum field theory and string theory that uses supersymmetry to exactly analyze strongly coupled gauge theories, leading to profound insights into dualities and four-dimensional topology.
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: Wess–Zumino–Witten model
Target entity description: 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.

A. Chern–Simons theory
Chern–Simons theory is a topological quantum field theory in three dimensions that plays a central role in modern geometry, topology, and theoretical physics, particularly in the study of knot invariants and gauge fields.
B. Rozansky–Witten theory
Rozansky–Witten theory is a three-dimensional topological quantum field theory associated with hyperkähler manifolds that yields invariants of 3-manifolds and links via holomorphic symplectic geometry.
C. Donaldson–Witten theory
Donaldson–Witten theory is a four-dimensional topological quantum field theory derived from twisting N=2 supersymmetric Yang–Mills theory, used to compute Donaldson invariants of smooth four-manifolds.
D. Witten index
The Witten index is a topological invariant in supersymmetric quantum field theory that counts the difference between bosonic and fermionic zero-energy states, providing insight into supersymmetry breaking.
E. Seiberg–Witten theory
Seiberg–Witten theory is a framework in quantum field theory and string theory that uses supersymmetry to exactly analyze strongly coupled gauge theories, leading to profound insights into dualities and four-dimensional topology.
F. None of above. chosen

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 ⓘ Edward Witten ⓘ Julius Wess ⓘ
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 ⓘ linked to: Wess–Zumino–Witten model topological term ⓘ
hasTopologicalFeature	action defined modulo 2π times an integer ⓘ
namedAfter	Bruno Zumino ⓘ Edward Witten ⓘ Julius Wess ⓘ
quantizesTo	discrete allowed levels from topological term ⓘ
relatedTo	Chern–Simons theory ⓘ bosonization ⓘ current algebra representations ⓘ modular invariance in conformal field theory ⓘ nonlinear sigma model ⓘ
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 ⓘ

How these facts were elicited