Wakimoto realizations of current and exchange algebras

TL;DR

This paper extends Wakimoto realizations from Lie algebra currents to group-valued chiral fields with monodromy, exploring their exchange algebra and related structures in the context of Poisson brackets.

Contribution

It introduces a Wakimoto realization for group-valued chiral fields with monodromy, expanding the algebraic framework of current and exchange algebra representations.

Findings

Extended Wakimoto realization to group-valued fields

Derived exchange algebra for monodromy-dependent fields

Reviewed the algebraic structure of the exchange relations

Abstract

Working at the level of Poisson brackets, we describe the extension of the generalized Wakimoto realization of a simple Lie algebra valued current, J, to a corresponding realization of a group valued chiral primary field, b, that has diagonal monodromy and satisfies $Kb'=Jb$. The chiral WZNW field b is subject to a monodromy dependent exchange algebra, whose derivation is reviewed, too.