H(3)+ correlators from Liouville theory

TL;DR

This paper establishes a direct link between H(3)+ model correlators and Liouville theory, revealing new insights into their mathematical structure and connections to Riemann surface uniformization.

Contribution

It provides a simple expression for H(3)+ correlators in terms of Liouville theory and explores their relation to Gaudin Hamiltonians and Riemann surface uniformization.

Findings

Correlation functions of H(3)+ model expressed via Liouville theory

Connection between KZ and BPZ equations established

Implications for eigenvectors of Gaudin Hamiltonians

Abstract

We prove that arbitrary correlation functions of the H(3)+ model on a sphere have a simple expression in terms of Liouville theory correlation functions. This is based on the correspondence between the KZ and BPZ equations, and on relations between the structure constants of Liouville theory and the H(3)+ model. In the critical level limit, these results imply a direct link between eigenvectors of the Gaudin Hamiltonians and the problem of uniformization of Riemann surfaces. We also present an expression for correlation functions of the SL(2)/U(1) coset model in terms of correlation functions in Liouville theory.