Free field representations for the affine superalgebra sl(2|1)

TL;DR

This paper constructs free field (Wakimoto) representations for the affine superalgebra sl(2|1) at level k, clarifying the relationship between two inequivalent root choices, with applications to noncritical N=2 string theory.

Contribution

It provides explicit Wakimoto representations for both root choices of the affine superalgebra sl(2|1) and establishes their quantum relation, advancing the understanding of superalgebra representations.

Findings

Constructed Wakimoto representations for each root choice.

Derived the quantum relation between the two representations.

Facilitated applications to noncritical N=2 string theory.

Abstract

Free field representations of the affine superalgebra $A(1,0)^{(1)}$ at level $k$ are needed in the description of the noncritical $N=2$ string. The superalgebra admits two inequivalent choices of simple roots. We give the Wakimoto representations corresponding to each of these and derive the relation between the two at the quantum level.