On some simple orbifold affine VOAs at non-admissible level arising from rank one 4D SCFTs
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
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2024
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| author | Arakawa, Tomoyuki Dai, Xuanzhong Fasquel, Justine Li, Bohan Moreau, Anne |
| author_facet | Arakawa, Tomoyuki Dai, Xuanzhong Fasquel, Justine Li, Bohan Moreau, Anne |
| contents | 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 Adamović and Perše 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04472 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On some simple orbifold affine VOAs at non-admissible level arising from rank one 4D SCFTs Arakawa, Tomoyuki Dai, Xuanzhong Fasquel, Justine Li, Bohan Moreau, Anne Representation Theory High Energy Physics - Theory Quantum Algebra 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 Adamović and Perše 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. |
| title | On some simple orbifold affine VOAs at non-admissible level arising from rank one 4D SCFTs |
| topic | Representation Theory High Energy Physics - Theory Quantum Algebra |
| url | https://arxiv.org/abs/2403.04472 |