SU(2) WZNW Model at Higher Genera from Gauge Field Functional Integral

TL;DR

This paper computes the gauge field functional integral for SU(2) Chern-Simons states on higher genus surfaces, enabling explicit expressions for higher genus WZNW partition functions and offering insights into Liouville theory.

Contribution

It provides a novel explicit finite-dimensional integral representation for higher genus SU(2) WZNW partition functions from gauge field integrals.

Findings

Explicit finite-dimensional integrals for higher genus partition functions

Connection established between Chern-Simons gauge integrals and WZNW conformal blocks

Potential implications for understanding Liouville theory's functional integral

Abstract

We compute the gauge field functional integral giving the scalar product of the SU(2) Chern-Simons theory states on a Riemann surface of genus > 1. The result allows to express the higher genera partition functions of the SU(2) WZNW conformal field theory by explicit finite dimensional integrals. Our calculation may also shed new light on the functional integral of the Liouville theory.