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Conformal embeddings and affine vertex operator algebras at negative integer levels

We study the problem of conformal embeddings of affine vertex operator algebras in $W$-algebras.We present a result on the classification of conformal embeddings of affine vertex algebras into minimal affine W-algebras and study some related problems. We will show that the corresponding branching rules are related to the representation theory of affine vertex algebras at negative levels and their fusion rules. New simple current modules and simple current extensions will be constructed. (This talk is based on joint papers with V. G. Kac, P. Moseneder Frajria, P. Papi and O. Perse)

conformal embeddings, W-algebras

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