$gl(2|2)$ Current Superalgebra and Non-unitary Conformal Field Theory

TL;DR

This paper explores the $gl(2|2)$ current superalgebra, providing its free field representation, energy-momentum tensor, and screen currents, with applications to disordered systems and non-unitary conformal field theories.

Contribution

It introduces a free field realization and Sugawara construction for the $gl(2|2)$ superalgebra at arbitrary level, including explicit screen currents, advancing the understanding of related non-unitary CFTs.

Findings

Constructed free field representation of $gl(2|2)$

Derived Sugawara energy-momentum tensor in non-standard basis

Presented three screen currents of the first kind

Abstract

Motivated by application of current superalgebras in the study of disordered systems such as the random XY and Dirac models, we investigate $gl(2|2)$ current superalgebra at general level $k$. We construct its free field representation and corresponding Sugawara energy-momentum tensor in the non-standard basis. Three screen currents of the first kind are also presented.