# nLab Witten index

Contents

### Context

#### Index theory

index theory, KK-theory

noncommutative stable homotopy theory

partition function

genus, orientation in generalized cohomology

## Definitions

operator K-theory

K-homology

supersymmetry

# Contents

## Idea

The Witten index or supersymmetric index of a supersymmetric quantum field theory is its partition function with the trace-operation replaced by the super-trace.

## Examples

The Witten index of the superstring is the Witten genus of the corresponding target space.

## References

### For $D=2$

For the superstring D=2 CFT:

See at Witten genus.

### For $D=3$$\mathcal{N}=4$ SYM

using discussion in

### For $D=4$$\mathcal{N}=1$ SYM

• Leonardo Rastelli, Shlomo S. Razamat, The supersymmetric index in four dimensions, Journal of Physics A: Mathematical and Theoretical, Volume 50, Number 44 (arXiv:1608.02965)

Last revised on January 2, 2020 at 03:54:45. See the history of this page for a list of all contributions to it.