Wakimoto realization of the quantum affine superalgebra $U_q(\widehat{sl}(M|N))$

TL;DR

This paper develops a bosonization framework for the quantum affine superalgebra $U_q(\\widehat{sl}(M|N))$ using Wakimoto realization and $\\xi-\ ext{eta}$ systems, applicable at arbitrary levels and connecting to classical limits.

Contribution

It introduces a new bosonization method for $U_q(\widehat{sl}(M|N))$ with explicit Wakimoto realization and screening operators for general levels.

Findings

Provides Wakimoto realization using $\\xi-\ ext{eta}$ system.

Constructs screening operators commuting with the superalgebra.

Derives a new bosonization of the affine superalgebra in the classical limit.

Abstract

A bosonization of the quantum affine superalgebra $U_q(\widehat{sl}(M|N))$ is presented for an arbitrary level $k \in {\bf C}$.The Wakimoto realization is given by using $\xi-\eta$ system. The screening operators that commute with $U_q(\widehat{sl}(M|N))$ are presented for the level $k \neq -M+N$. New bosonization of the affine superalgebra $\widehat{sl}(M|N)$ is obtained in the limit $q \to 1$.