Exact Operator Solution of $A_2$-Toda Field Theory

TL;DR

This paper develops an exact operator solution for quantum $A_2$-Toda field theory in two dimensions, using canonical free field quantization and constructing exponential operators to the fourth order, leading to a conjecture for the full solution.

Contribution

It introduces a method to construct Toda exponential operators to the fourth order and proposes a conjecture for the exact operator solution in quantum $A_2$-Toda field theory.

Findings

Constructed exponential operators up to fourth order in the cosmological constant.

Proposed a conjecture for the exact operator solution based on these constructions.

Advanced the understanding of quantum $A_2$-Toda field theory in two dimensions.

Abstract

Quantum $A_2$-Toda field theory in two dimensions is investigated based on the method of quantizing canonical free field. Toda exponential operators associated with the fundamental weights are constructed to the fourth order in the cosmological constant. This leads us to a conjecture for the exact operator solution.