Localization in GWZW and Verlinde formula

TL;DR

This paper demonstrates that gauged Wess-Zumino-Witten theory with compact groups can be exactly solved via localization, exemplified by deriving the Verlinde formula for SU(2) on Riemann surfaces.

Contribution

It introduces a localization approach to exactly solve gauged WZW theories, connecting them to the Verlinde formula for conformal blocks.

Findings

Exact functional integral calculation for SU(2) on Riemann surfaces

Establishment of fermionic BRST-like symmetry in gauged WZW theory

Derivation of Verlinde formula as a special case

Abstract

Gauged Wess-Zumino-Witten theory for compact groups is considered. It is shown that this theory has fermionic BRST-like symmetry and may be exactly solved using localization approach. As an example we calculate functional integral for the case of SU(2) group on the arbitrary Riemann surface. The answer is the particular case of Verlinde formula for the number of conformal blocks.