nLab Witten index

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

General

See also

• Wikipedia, Witten index

For $D=2$

For the superstring D=2 CFT:

See at Witten genus.

For $D=3$ $\mathcal{N}=1$ SYM

For D=3 N=1 super Yang-Mills theory:

• Edward Witten, Supersymmetric Index Of Three-Dimensional Gauge Theory, in: The many faces of the superworld_ (arXiv:hep-th/9903005)

For $D=3$ $\mathcal{N}=2$ SYM

For D=3 N=2 super Yang-Mills theory:

• Mathew Bullimore, Andrea E. V. Ferrari, Heeyeon Kim, The 3d Twisted Index and Wall-Crossing (arXiv:1912.09591)

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

For D=3 N=4 super Yang-Mills theory:

• Mathew Bullimore, Andrea E.V. Ferrari, Heeyeon Kim, Twisted Indices of 3d N=4 Gauge Theories and Enumerative Geometry of Quasi-Maps (arXiv:1812.05567)

• Davide Gaiotto, Tadashi Okazaki, Sphere correlation functions and Verma modules (arXiv:1911.11126)

using discussion in

• Andrei Okounkov, Section 3.4 of: Lectures on K-theoretic computations in enumerative geometry (arXiv:1512.07363)

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

For D=4 N=1 super Yang-Mills theory:

• 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)