Conformal embeddings of affine vertex algebras in minimal W-algebras I: Structural results

By Dražen Adamović, V. Kac, Pierluigi Möseneder Frajria, Paolo Papi, Ozren Perše. 2016

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Abstract We find all values of k ∈ C , for which the embedding of the maximal affine vertex algebra in a simple minimal W-algebra W k ( g , θ ) is conformal, where g is a basic simple Lie superalgebra and −θ its minimal root. In particular, it turns out that if W k ( g , θ ) does not collapse to its affine part, then the possible values of these k are either − 2 3 h ∨ or − h ∨ − 1 2 , where h ∨ is the dual Coxeter number of g for the normalization ( θ , θ ) = 2 . As an application of our results, we present a realization of simple affine vertex algebra V − n + 1 2 ( s l ( n + 1 ) ) inside the tensor product of the vertex algebra W n − 1 2 ( s l ( 2 | n ) , θ ) (also called the Bershadsky–Knizhnik algebra) with a lattice vertex algebra.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7afdf674c16b9d7dc0110ea5b66e9b76af34f50f