Classical Wakimoto Realizations of Chiral WZNW Bloch Waves

TL;DR

This paper derives the classical exchange algebra for chiral WZNW Bloch waves by inverting the symplectic form and constructs generalized free field realizations extending Wakimoto's current algebra representations.

Contribution

It provides a direct derivation of the exchange algebra and introduces a systematic method for constructing generalized free field realizations.

Findings

Derived the exchange algebra by symplectic form inversion.

Constructed generalized free field realizations extending Wakimoto's approach.

Established a systematic algorithm for realization construction.

Abstract

It is well-known that the chiral WZNW Bloch waves satisfy a quadratic classical exchange algebra which implies the affine Kac-Moody algebra for the corresponding currents. We here obtain a direct derivation of the exchange algebra by inverting the symplectic form on the space of Bloch waves, and give a completely algorithmic construction of its generalized free field realizations that extend the classical Wakimoto realizations of the current algebra.