Berezin Quantization of Gauged WZW and Coset Models

TL;DR

This paper explores the use of Berezin quantization for gauged WZW and coset models, revealing holomorphic factorization properties in the quantization process related to the moduli space's complex structure.

Contribution

It introduces a Berezin quantization approach for gauged WZW and coset models, highlighting holomorphic factorization in the quantization framework.

Findings

Holomorphic factorization in Berezin quantization of gauged models

Quantization procedure compatible with complex structure of moduli space

Enhanced understanding of the mathematical structure of gauged models

Abstract

Gauged WZW and coset models are known to be useful to prove holomorphic factorization of the partition function of WZW and coset models. In this note we show that these gauged models can be also important to quantize the theory in the context of the Berezin formalism. For gauged coset models Berezin quantization procedure also admits a further holomorphic factorization in the complex structure of the moduli space.