On the Three-Point Couplings in Toda Field Theory

TL;DR

This paper extends the understanding of three-point couplings in Toda field theory by generalizing known relations from Liouville theory and deriving explicit two- and three-point functions for Toda vertices.

Contribution

It introduces a method to compute Toda field theory correlation functions by generalizing Liouville theory techniques to arbitrary Toda models.

Findings

Derived explicit two-point functions for Toda vertices.

Obtained three-point functions associated with simple roots.

Generalized Liouville relations to Toda theories.

Abstract

Correlation functions of Toda field vertices are investigated by applying the method of integrating zero-mode developed for Liouville theory. We generalize the relations among the zero-, two- and three-point couplings known in Liouville case to arbitrary Toda theories. Two- and three-point functions of Toda vertices associated with the simple roots are obtained.