Bantay's trace in unitary modular tensor categories

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) [2]. The trace is another invariant for UMTCs which depends only on modular data, and contains the expression of the Frobenius-Schur indicator [21] 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.