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arXiv · hep-th/9512092

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

A M Semikhatov·I Yu Tipunin
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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.

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A M Semikhatov, I Yu Tipunin. 1995-12-13. $sl(2)_{-4}$ WZW Model as an N=4 Supersymmetric Bosonic String with $c=-2$ matter. https://doi.org/10.1142/s0217751x96001322

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