A Kac-Weyl Character Identity

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.

8 pages

References in corpus (8)

• Rank-finiteness for modular categories
• Kac-Moody and Virasoro Characters from the Perturbative Chern-Simons Path Integral
• Fusion Potentials for G_k and Handle Squashing
• Partition Functions of Chern-Simons Theory on Handlebodies by Radial Quantization
• On sums of tensor and fusion multiplicities
• On conformal field theories with low number of primary fields
• Conjugation Properties of Tensor Product and Fusion Coefficients
• Handle Operators of Coset Models