Free field realization of current superalgebra $gl(m|n)_k$

TL;DR

This paper develops a free field representation for the current superalgebra $gl(m|n)_k$, including affine currents, energy-momentum tensor, and screening currents, applicable for both $m=n$ and $m eq n$ cases.

Contribution

It provides a unified construction of free field representations for $gl(m|n)_k$ superalgebra, incorporating the energy-momentum tensor from two Sugawara tensors.

Findings

Constructed free field representation for $gl(m|n)_k$ superalgebra.

Derived energy-momentum tensor from two Sugawara tensors.

Applicable to both $m=n$ and $m eq n$ cases.

Abstract

We construct the free field representation of the affine currents, energy-momentum tensor and screening currents of the first kind of the current superalgebra $gl(m|n)_k$ uniformly for $m=n$ and $m\neq n$. The energy-momentum tensor is given by a linear combination of two Sugawara tensors associated with the two independent quadratic Casimir elements of $gl(m|n)$.