Parafermionic polynomials, Selberg integrals and three-point correlation function in parafermionic Liouville field theory

TL;DR

This paper develops a method to compute three-point correlation functions in parafermionic Liouville field theory exactly, using integral representations and Selberg integrals with parafermionic polynomials, supported by dual model approaches.

Contribution

It introduces a novel exact computation technique for correlation functions in parafermionic Liouville theory via generalized Selberg integrals.

Findings

Derived explicit integral representations for three-point functions.

Evaluated generalized Selberg integrals with parafermionic polynomials.

Validated results through dual model analysis.

Abstract

In this paper we consider parafermionic Liouville field theory. We study integral representations of three-point correlation functions and develop a method allowing us to compute them exactly. In particular, we evaluate the generalization of Selberg integral obtained by insertion of parafermionic polynomial. Our result is justified by different approach based on dual representation of parafermionic Liouville field theory described by three-exponential model.