Bantay's trace in Unitary Modular Tensor Categories

TL;DR

This paper proves a trace formula for self-braidings in unitary modular tensor categories, linking it to modular data and applications in classifying these categories and their realizability.

Contribution

It provides a rigorous proof of a trace formula for self-braidings in UMTCs, connecting it to modular data and extending the Frobenius-Schur indicator.

Findings

Trace formula depends only on modular data

Trace is an invariant in UMTCs

Applications to UMTC classification and realizability

Abstract

We give a proof of a formula for the trace of self-braidings (in an arbitrary channel) in UMTCs which first appeared in the context of rational conformal field theories (CFTs). The trace is another invariant for UMTCs which depends only on modular data, and contains the expression of the Frobenius-Schur indicator as a special case. Furthermore, we discuss some applications of the trace formula to the realizability problem of modular data and to the classification of UMTCs.