$sl(2)_{-4}$ WZW Model as an N=4 Supersymmetric Bosonic String with $c=-2$ matter

TL;DR

This paper explores the sl(2)_{-4} WZW model's connection to an N=4 supersymmetric bosonic string with c=-2 matter, revealing new algebraic structures and cohomological relations.

Contribution

It formulates a spectral sequence for the sl(2)_{-4} model's BRST cohomology and uncovers an N=4 algebra within a c=-2 bosonic string framework, establishing a novel link between these models.

Findings

Identification of N=4 algebra in the spectral sequence

Realization of cohomology as Q_{string}-primitives of singular vectors

Explicit operator construction linking sl(2)_{-4} WZW and c=-2 string

Abstract

We consider the sl(2) current algebra at level k=-4 when the sl(2) BRST operator is nilpotent. We formulate a spectral sequence converging to the cohomology of this BRST operator. At the second term of the spectral sequence, we observe an N=4 algebra. This algebra is generated in a c=-2 bosonic string whose BRST operator Q_{string} represents the next term in the spectral sequence. We realize the cohomology of the irreducible modules as Q_{string}-primitives of the N=4 singular vectors and point out their relation to Lian--Zuckerman states of c=-2 matter. The relation between sl(2)_{-4} WZW model and c=-2 bosonic string is established both at the level of BRST cohomology and at the level of an explicit operator construction. The relation of the N=4 algebra to the known symmetries of matter+gravity systems is also investigated.