Luca Giorgetti, Karl-Henning Rehren
June 14, 2016
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.
Keywords:modular categories, braided tensor *-category, modular data, rational conformal field theories, Frobenius-Schur indicator