Remarks on A_2 Toda Field Theory

TL;DR

This paper investigates the A_2 Toda field theory, revealing that after zero mode integration, correlation functions resemble free theories, and deriving functional equations for structure constants using differential equations and crossing symmetry.

Contribution

It extends the Goulian-Li technique to finite Lie algebras and derives new functional equations for A_2 Toda structure constants.

Findings

Correlation functions resemble free theories after zero mode integration.

Four-point functions with degenerate fields satisfy Riemann differential equations.

Functional equations for structure constants are derived from crossing symmetry.

Abstract

We study the Toda field theory with finite Lie algebras using an extension of the Goulian-Li technique. In this way, we show that, after integrating over the zero mode in the correlation functions of the exponential fields, the resulting correlation function resembles that of a free theory. Furthermore, it is shown that for some ratios of the charges of the exponential fields the four-point correlation functions which contain a degenerate field satisfy the Riemann ordinary differential equation. Using this fact and the crossing symmetry, we derive a set of functional equations for the structure constants of the A_2 Toda field theory.