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On some simple orbifold affine VOAs at non-admissible level arising from rank one 4D SCFTs (2403.04472v2)

Published 7 Mar 2024 in math.RT, hep-th, and math.QA

Abstract: We study the representations of some simple affine vertex algebras at non-admissible level arising from rank one 4D SCFTs. In particular, we classify the irreducible highest weight modules of $L_{-2}(G_2)$ and $L_{-2}(B_3)$. It is known by the works of Adamovi\'{c} and Per\v{s}e that these vertex algebras can be conformally embedded into $L_{-2}(D_4)$. We also compute the associated variety of $L_{-2}(G_2)$, and show that it is the orbifold of the associated variety of $L_{-2}(D_4)$ by the symmetric group of degree 3 which is the Dynkin diagram automorphism group of $D_4$. This provides a new interesting example of associated variety satisfying a number of conjectures in the context of orbifold vertex algebras.

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