Localization in GWZW and Verlinde formula

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.