nLab
Witten index

Contents

Context

Index theory

Super-Geometry

Quantum Field Theory

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)

Introduction

Concepts

field theory:

Lagrangian field theory

quantization

quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization

renormalization

Theorems

States and observables

Operator algebra

Local QFT

Perturbative QFT

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

General

See also

For D=2D=2

For the superstring D=2 CFT:

See at Witten genus.

For D=3D=3 𝒩=1\mathcal{N}=1 SYM

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

For D=3D=3 𝒩=2\mathcal{N}=2 SYM

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

For D=3D=3 𝒩=4\mathcal{N}=4 SYM

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

using discussion in

For D=4D=4 𝒩=1\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)

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