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 |
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 ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.