Ozren Perse

Some General Results on Conformal Embeddings of Affine Vertex Operator Algebras

We give a general criterion for conformal embeddings of vertex operator algebras associated to affine Lie algebras at arbitrary levels. Using that criterion, we construct new conformal embeddings at admissible rational and negative integer levels. In particular, we construct all remaining conformal embeddings associated to automorphisms of Dynkin diagrams of simple Lie algebras. The semisimplicity of the corresponding decompositions is obtained by using the concept of fusion rules for vertex operator algebras.

Conformal embeddings of affine vertex algebras in minimal

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.

W

Building on work of the first and last author, we prove that an embedding of simple affine vertex algebras

Finite vs. Infinite Decompositions in Conformal Embeddings

{V_{\mathbf{k}}({\mathfrak{g}}^0)\subset V_{k}({\mathfrak{g}})}

The Vertex Algebra

Vk(g0)⊂Vk(g), corresponding to an embedding of a maximal equal rank reductive subalgebra

and Certain Affine Vertex Algebras of Level -1

{{\mathfrak{g}}^0}