Primary fields and screening currents of gl(2|2) non-unitary conformal field theory

TL;DR

This paper constructs primary fields and screening currents for the non-unitary conformal field theory based on the non-semisimple gl(2|2) superalgebra, providing explicit formulas in terms of free fields.

Contribution

It introduces explicit constructions of primary fields and screening currents for the gl(2|2) superalgebra-based conformal field theory, advancing understanding of its structure.

Findings

Explicit primary fields for all finite-dimensional irreducible representations

Three screening currents of the first kind constructed explicitly

Framework for analyzing non-unitary gl(2|2) conformal field theories

Abstract

The non-semisimple $gl(2|2)_k$ current superalgebra in the standard basis and the corresponding non-unitary conformal field theory are investigated. Infinite families of primary fields corresponding to all finite-dimensional irreducible typical and atypical representations of $gl(2|2)$ and three (two even and one odd) screening currents of the first kind are constructed explicitly in terms of ten free fields.