Consistently Constrained SL(N) WZWN Models and Classical Exchange Algebra

TL;DR

This paper investigates constrained SL(N) WZWN models, establishing their Poisson structures, demonstrating the Virasoro algebra, and constructing conformal primaries that satisfy quadratic and potential exchange algebras.

Contribution

It introduces a consistent framework for constrained SL(N) WZWN models, deriving their Poisson brackets and exploring their algebraic structures including the Virasoro and exchange algebras.

Findings

Poisson brackets satisfy Jacobi identities via classical Yang-Baxter equation

Virasoro algebra is realized within the constrained models

Constructed SL(N) conformal primary with quadratic algebra

Abstract

Currents of the SL(N) WZWN model are constrained so that the remaining symmetry is a symmetry of constrained currents as well. Such consistency enables us to study the Poisson structure of constrained SL(N) WZWN models properly. We establish the Poisson brackets which satisfy the Jacobi identities owing to the classical Yang-Baxter equation. The Virasoro algebra is shown by using them. An SL(N) conformal primary is constructed. It satisfies a quadratic algebra, which might become an exchange algebra by its quantum deformation.