A Kac-Weyl Character Identity

TL;DR

This paper derives a Kac-Weyl character identity from quantized Chern-Simons theory, providing new tools to analyze fusion coefficients and symmetries in rational conformal field theories.

Contribution

It introduces an explicit character identity that constrains fusion coefficients and reveals conjugacy symmetries in current algebra-based RCFTs.

Findings

Derived inequalities for fusion coefficients

Established conjugacy symmetry of fusion coefficient sums

Linked Chern-Simons quantization to character identities

Abstract

An explicit quantization of Chern-Simons theory leads to an identity between sums of the Kac-Weyl characters. One can use this identity to prove inequalities that constrain the fusion coefficients $N_{\mu\nu}^l$ in the case of RCFTs that descend from current algebras. It also leads to a statement regarding the conjugacy symmetry of the sums of squares of fusion coefficients for current algebras admitting complex representations.