On the Lagrangian Realization of the WZNW Reductions

TL;DR

This paper presents a phase space path-integral method to derive Lagrangian formulations of models obtained from Hamiltonian reduction of WZNW theory, unifying several known models under this framework.

Contribution

It introduces a systematic approach to derive Lagrangian realizations of WZNW reduction models, connecting various known actions within a unified formalism.

Findings

Derived Sonnenschein's action as a Lagrangian realization.

Connected generalized Toda action to WZNW reductions.

Unified gauged WZNW model within the phase space path-integral approach.

Abstract

We develop a phase space path-integral approach for deriving the Lagrangian realization of the models defined by Hamiltonian reduction of the WZNW theory. We illustrate the uses of the approach by applying it to the models of non-Abelian chiral bosons, $W$-algebras and the GKO coset construction, and show that the well-known Sonnenschein's action, the generalized Toda action and the gauged WZNW model are precisely the Lagrangian realizations of those models, respectively.