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.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Wess–Zumino–Witten conformal field theory | 1 |
| Wess–Zumino–Witten model canonical | 1 |
| Wess–Zumino–Witten term | 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
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 ⓘ |
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: Wess–Zumino–Witten model Description of subject: 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.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Wess–Zumino–Witten conformal field theory
subject surface form:
't Hooft anomaly
this entity surface form:
Wess–Zumino–Witten term