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

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.

LaTeX 2.09, 23 pages, no figures

References in corpus (4)

• Quasi-particles models for the representations of Lie algebras and geometry of flag manifold
• Singular Vectors of the Topological Conformal Algebra
• Coset Construction and Character Sumrules for the Doubly Extended $N=4$ Superconformal Algebras
• Construction of BRST invariant states in $G/H$ WZNW models.

Cited by in corpus (2)

• Disordered Dirac Fermions: the Marriage of Three Different Approaches
• N=2 structures in all string theories