The Frobenius-Schur indicator in Conformal Field Theory

TL;DR

This paper introduces a Frobenius-Schur indicator analogue in Conformal Field Theory to classify primary fields as real or pseudo-real, providing an explicit trace-based formula.

Contribution

It develops a new invariant in Conformal Field Theory to distinguish types of self-conjugate primary fields, extending classical concepts.

Findings

Derived an explicit trace formula for the indicator

Classified primary fields as real or pseudo-real

Extended classical Frobenius-Schur concepts to CFT

Abstract

An analogue of the classical Frobenius-Schur indicator is introduced in order to distinguish between real and pseudo-real self-conjugate primary fields, and an explicit expression for this quantity is derived from the trace of the braiding operator.