Crossing Symmetry in the $H_3^+$ WZNW model

TL;DR

This paper demonstrates that crossing symmetry in the $H_3^+$ WZNW model can be derived from known properties of five-point functions in Liouville theory, establishing a connection between the two models.

Contribution

It establishes a link between crossing symmetry in the $H_3^+$ WZNW model and Liouville theory, providing a new proof based on existing Liouville correlation functions.

Findings

Crossing symmetry in the $H_3^+$ WZNW model is derived from Liouville theory properties.

The proof relies on the relation between four-point functions in $H_3^+$ and five-point functions in Liouville theory.

The approach simplifies understanding of crossing symmetry in the WZNW model.

Abstract

We show that crossing symmetry of four point functions in the $H_3^+$ WZNW model follows from similar properties of certain five point correlation functions in Liouville theory that have already been proven previously.