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

Tomoyuki Arakawa; Xuanzhong Dai; Justine Fasquel; Bohan Li; Anne Moreau

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arXiv · 2403.04472

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

Tomoyuki Arakawa·Xuanzhong Dai·Justine Fasquel·Bohan Li·Anne Moreau

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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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BibTeX RIS

Tomoyuki Arakawa, Xuanzhong Dai, Justine Fasquel, Bohan Li, Anne Moreau. 2024-03-07. On some simple orbifold affine VOAs at non-admissible level arising from rank one 4D SCFTs. https://arxiv.org/abs/2403.04472

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