paper

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

arXiv:2403.04472

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 AdamoviÄ and PerÅ¡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.

33 pages, to appear in Commun. Math. Physics