Witten index
E244832
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Witten index canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T2227987 — 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: Witten index Context triple: [Edward Witten, notableWork, Witten index]
-
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.
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B.
Atiyah–Singer index theorem
The Atiyah–Singer index theorem is a fundamental result in mathematics that links the analytical properties of elliptic differential operators to topological invariants of manifolds, unifying analysis, topology, and geometry.
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C.
Pauli–Villars regularization
Pauli–Villars regularization is a technique in quantum field theory that controls ultraviolet divergences by introducing auxiliary heavy fields to render integrals finite.
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D.
Wick’s theorem
Wick’s theorem is a fundamental result in quantum field theory that expresses time-ordered products of field operators as sums of normal-ordered products with all possible contractions, forming the basis for deriving Feynman rules and diagrammatic expansions.
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E.
topological quantum field theory
A topological quantum field theory is a quantum field theory whose observables and correlation functions depend only on the topology of the underlying spacetime manifold rather than its geometric details, making it a powerful tool in both mathematics and theoretical physics.
- 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: Witten index Target entity description: 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.
-
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.
Atiyah–Singer index theorem
The Atiyah–Singer index theorem is a fundamental result in mathematics that links the analytical properties of elliptic differential operators to topological invariants of manifolds, unifying analysis, topology, and geometry.
-
C.
Pauli–Villars regularization
Pauli–Villars regularization is a technique in quantum field theory that controls ultraviolet divergences by introducing auxiliary heavy fields to render integrals finite.
-
D.
Wick’s theorem
Wick’s theorem is a fundamental result in quantum field theory that expresses time-ordered products of field operators as sums of normal-ordered products with all possible contractions, forming the basis for deriving Feynman rules and diagrammatic expansions.
-
E.
topological quantum field theory
A topological quantum field theory is a quantum field theory whose observables and correlation functions depend only on the topology of the underlying spacetime manifold rather than its geometric details, making it a powerful tool in both mathematics and theoretical physics.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
supersymmetry index
ⓘ
topological invariant ⓘ |
| appliesTo | theories with discrete energy spectrum ⓘ |
| canBeComputedBy |
path integral with periodic boundary conditions for fermions
ⓘ
supersymmetric localization ⓘ |
| counts | bosonic zero-energy states minus fermionic zero-energy states ⓘ |
| definedAs | Tr((-1)^F e^{-\beta H}) ⓘ |
| dependsOn | spectrum of the Hamiltonian ⓘ |
| generalizedTo |
elliptic genus
ⓘ
refined indices ⓘ superconformal index ⓘ |
| hasParameter | inverse temperature parameter beta ⓘ |
| hasProperty |
insensitive to small perturbations preserving supersymmetry
ⓘ
integer-valued ⓘ topologically protected ⓘ |
| hasPurpose |
to count the difference between bosonic and fermionic zero-energy states
ⓘ
to diagnose supersymmetry breaking ⓘ |
| independentOf | beta for supersymmetric theories with discrete spectrum ⓘ |
| indicates |
possible supersymmetry breaking when zero
ⓘ
unbroken supersymmetry when nonzero ⓘ |
| introducedBy | Edward Witten ⓘ |
| introducedInContextOf | supersymmetric quantum mechanics ⓘ |
| invariantUnder |
continuous deformations of parameters
ⓘ
renormalization group flow ⓘ |
| mathematicallyRelatedTo |
Atiyah–Singer index theorem
ⓘ
index of an elliptic operator ⓘ |
| namedAfter | Edward Witten ⓘ |
| relatedConcept |
BPS state counting
ⓘ
central charges in supersymmetry ⓘ |
| relatedTo |
Hamiltonian
ⓘ
fermion number operator ⓘ partition function on Euclidean time circle with periodic fermions ⓘ supersymmetry generators ⓘ |
| requires | well-defined Hilbert space of states ⓘ |
| robustAgainst | quantum corrections ⓘ |
| usedIn |
analysis of domain walls
ⓘ
analysis of instantons ⓘ analysis of monopoles ⓘ analysis of supersymmetric solitons ⓘ four-dimensional supersymmetric field theories ⓘ gauge theory ⓘ string theory ⓘ supersymmetric quantum field theory ⓘ supersymmetric quantum mechanics ⓘ two-dimensional supersymmetric field theories ⓘ |
| usedToTest |
existence of supersymmetric ground states
ⓘ
stability of supersymmetric vacua ⓘ |
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: Witten index Description of subject: 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.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.