Integrability of the Wess_Zumino-Witten model as a non-ultralocal theory

TL;DR

This paper investigates the integrability of the 2D Wess--Zumino--Witten model using an $r$--$s$ matrix approach, revealing a new non--dynamical $r$ matrix in the Poisson algebra of conserved quantities.

Contribution

It introduces a novel non--dynamical $r$ matrix approach to analyze the non--ultralocal structure of the WZW model's Poisson algebra.

Findings

Derived the Poisson algebra of monodromy matrices.

Identified a new non--dynamical $r$ matrix.

Extended the $r$--$s$ matrix formalism to non--ultralocal theories.

Abstract

We consider the 2--dimensional Wess--Zumino--Witten (WZW) model in the canonical formalism introduced in a previous paper by two of us. Using an $r$--$s$ matrix approach to non--ultralocal field theories we find the Poisson algebra of monodromy matrices and of conserved quantities with a new, non--dynamical, $r$ matrix.