H^+_3 WZNW model from Liouville field theory

TL;DR

This paper establishes a path integral derivation linking correlation functions in the H^+_3 WZNW model to Liouville field theory, extending the relation to higher genus surfaces and providing explicit formulas for primary field correlators.

Contribution

It introduces a new path integral approach to relate WZNW and Liouville theories and generalizes the correlation function correspondence to arbitrary genus surfaces.

Findings

Derived explicit WZNW correlators via Liouville correlators with degenerate insertions

Extended the known genus zero relation to surfaces of any genus

Provided a framework for further exploration of geometric Langlands connections

Abstract

There exists an intriguing relation between genus zero correlation functions in the H^+_3 WZNW model and in Liouville field theory. We provide a path integral derivation of the correspondence and then use our new approach to generalize the relation to surfaces of arbitrary genus g. In particular we determine the correlation functions of N primary fields in the WZNW model explicitly through Liouville correlators with N+2g-2 additional insertions of certain degenerate fields. The paper concludes with a list of interesting further extensions and a few comments on the relation to the geometric Langlands program.