WZW-Toda Reduction using the Casimir Operator

TL;DR

This paper develops a quantum Hamiltonian for the WZW model using the Casimir operator, enabling a straightforward reduction to Toda field theory and derivation of its quantum central charge.

Contribution

It introduces a novel quantum Hamiltonian formulation for the WZW model based on the Casimir operator, simplifying the reduction to Toda theory.

Findings

Quantum Hamiltonian constructed using Casimir operator

Simplified derivation of quantum central charge for Toda theory

Facilitates quantum reduction from WZW to Toda model

Abstract

We construct a quantum Hamiltonian operator for the Wess-Zumino-Witten (WZW) model in terms of the Casimir operator. This facilitates the discussion of the reduction of the WZW model to Toda field theory at the quantum level and provides a very straightforward derivation of the quantum central charge for the Toda field theory.