A2 Toda theory in reduced WZNW framework and the representations of the W algebra

TL;DR

This paper explores the classical and quantum structures of the A2 Toda theory using a reduced WZNW framework, revealing that the quantized fields align with minimal model representations of the W algebra.

Contribution

It introduces a novel analysis of the A2 Toda theory within a reduced WZNW framework and links the quantized fields to minimal model representations of the W algebra.

Findings

Classical solutions are classified by the W orbit structure.

Quantized Toda fields correspond to minimal model representations.

The local operator construction is consistent within a specific Hilbert space.

Abstract

Using the reduced WZNW formulation we analyse the classical $W$ orbit content of the space of classical solutions of the $A_2$ Toda theory. We define the quantized Toda field as a periodic primary field of the $W$ algebra satisfying the quantized equations of motion. We show that this local operator can be constructed consistently only in a Hilbert space consisting of the representations corresponding to the minimal models of the $W$ algebra.