Anyon Statistics and the Witten Index

TL;DR

This paper extends the Witten index to 2+1 dimensions within supersymmetric anyon theory, showing that despite complex contributions from anyonic states, the overall index remains integral, with significant implications.

Contribution

It introduces a generalized Witten index for supersymmetric anyons in 2+1 dimensions, accounting for anyon spin and statistics, and proves its integrality.

Findings

The index can have irrational and complex contributions from anyonic states.

The overall Witten index remains always integral.

Implications for supersymmetric theories with anyons.

Abstract

Using the theory of supersymmetric anyons, I extend the definition of the Witten index to 2+1 dimensions so as to accommodate the existence of anyon spin and statistics. I then demonstrate that, although in general the index receives irrational and complex contributions from anyonic states, the overall index is always integral, and I consider some of the implications and interpretations of this result.