This article is cited in 8 papers

The vertex algebra $m(1)^+$ and certain affine vertex algebras of level $-1$

Dražen Adamović, Ozren Perše

Faculty of Science, Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia

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 $L_{C_{\ell}^{(1)}}(-\frac12\Lambda_0)\otimes L_{C_{\ell} ^{(1)}}(-\frac{1}{2}\Lambda_0)$. 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 $L_{C_{\ell} ^{(1)}}(-\Lambda_0)$.

Keywords: vertex operator algebra, affine Kac–Moody algebra, coset vertex algebra, conformal embedding, $\mathcal W$-algebra.

MSC: 17B69; 17B67; 17B68; 81R10

Received: March 9, 2012; in final form July 1, 2012; Published online July 8, 2012

Language: English

DOI: 10.3842/SIGMA.2012.040

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ArXiv: 1006.1752