On a series of simple affine VOAs at non-admissible level arising from rank One 4D SCFTs

We study the representations of the 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 (G₂) and L-₂ (B₃). It is known by the works of Adamovi\'c and Perse that these vertex algebras can be conformally embedded into L-₂ (D₄). We also compute the associated variety of L-₂ (G₂), and show that it is the orbifold of the associated variety of L-₂ (D₄) by the symmetric group of degree 3 which is the Dynkin diagram automorphism group of D₄. This provides a new interesting example of associated variety satisfying a number of conjectures in the context of orbifold vertex algebras.