Bosonization of superalgebra $U_q(\widehat{sl}(N|1))$ for an arbitrary level

TL;DR

This paper develops a bosonization framework for the quantum affine superalgebra $U_q(\\widehat{sl}(N|1))$ at arbitrary levels, enabling new realizations and vertex operator constructions with applications to correlation functions.

Contribution

It introduces a novel bosonization for any level $k$, distinct from the level 1 case, and constructs Wakimoto and vertex operator realizations with screening operators.

Findings

Bosonization valid for all levels $k \\in \\mathbb{C}$

Construction of Wakimoto realization matching Verma module characters

Proposal of vertex operators and analysis of correlation functions

Abstract

We give a bosonization of the quantum affine superalgebra $U_q(\widehat{sl}(N|1))$ for an arbitrary level $k \in {\bf C}$. The bosonization of level $k \in {\bf C}$ is completely different from those of level $k=1$. From this bosonization, we induce the Wakimoto realization whose character coincides with those of the Verma module. We give the screening that commute with $U_q(\widehat{sl}(N|1))$. Using this screening, we propose the vertex operator that is the intertwiner among the Wakimoto realization and typical realization. We study non-vanishing property of the correlation function defined by a trace of the vertex operators.