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The Vertex Algebra $M(1)^+$ and Certain Affine Vertex Algebras of Level -1 (1006.1752v2)

Published 9 Jun 2010 in math.QA, math-ph, math.MP, and math.RT

Abstract: We give a coset realization of the vertex operator algebra $M(1)+$ with central charge $\ell$. We realize $M(1)+$ as a commutant of certain affine vertex algebras of level -1 in the vertex algebra $L_{C_{\ell} {(1)}}(-\tfrac{1}{2}\Lambda_0) \otimes L_{C_{\ell} {(1)}}(-\tfrac{1}{2}\Lambda_0)$. We show that the simple vertex algebra $L_{C_{\ell} {(1)}}(-\Lambda_0)$ can be (conformally) embedded into $L_{A_{2 \ell -1} {(1)}} (-\Lambda_0)$ and find the corresponding decomposition. We also study certain coset subalgebras inside $L_{C_{\ell} {(1)}}(-\Lambda_0)$.

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