Schwinger-Dyson approach to Liouville Field Theory

TL;DR

This paper applies the Schwinger-Dyson approach to Liouville field theory, deriving functional equations for the three-point structure constant and exploring their role in uniquely determining it.

Contribution

It introduces a dual Schwinger-Dyson framework for Liouville theory, deriving two functional equations that help fix the structure constant.

Findings

Derived a functional equation for the three-point structure constant.

Established a dual Schwinger-Dyson equation based on charge operator duality.

Proposed a method to uniquely determine the structure constant using these equations.

Abstract

We discuss Liouville field theory in the framework of Schwinger-Dyson approach and derive a functional equation for the three-point structure constant. We argue the existence of a second Schwinger-Dyson equation on the basis of the duality between the screening charge operators and obtain a second functional equation for the structure constant. We discuss the utility of the two functional equations to fix the structure constant uniquely.