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PreprintCC BY-NC-ND 4.0arXiv

On quasi-lisse affine vertex algebras L−1−h/6(g) from rank-one Argyres-Douglas theories

  • Drazen Adamovic
  • Xuanzhong Dai
  • Kaiwen Sun
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Abstract

We study certain simple affine vertex algebras L−1−h/6(g) from rank-one Argyres-Douglas theories, where g is a non-simply-laced simple Lie algebra and h is its Coxeter number. For L−3(F4), we determine the maximal ideal of V−3(F4), Zhu's algebra, and the associated variety. We also classify the irreducible highest-weight L−3(F4)-modules and determine the characters of its irreducible ordinary modules. The associated variety is 𝕆̅Ã1, and the level −3 is totally collapsing for the orbit 𝕆Ã1. The Poisson coinvariants of the C2-algebra of L−3(F4) are isomorphic to ℂ[ℓ]/(ℓ5), where ℓ is induced by the conformal vector. Consequently, the characters of ordinary L−3(F4)-modules satisfy a fifth-order modular linear differential equation. We also give modular linear differential equations of orders five and eleven satisfied by the characters of ordinary modules for L−2(B3) and L−2(G2) respectively.

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Cite

BibTeXRIS
BibTeX
@misc{adamovic2026quasilisse,
  title = {{On quasi-lisse affine vertex algebras $L_-1-h/6(\mathfrakg)$ from rank-one Argyres-Douglas theories}},
  author = {Drazen Adamovic and Xuanzhong Dai and Kaiwen Sun},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.17676},
  eprint = {2610.17676},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.17676},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - On quasi-lisse affine vertex algebras L_−1−h/6(g) from rank-one Argyres-Douglas theories
AU  - Drazen Adamovic
AU  - Xuanzhong Dai
AU  - Kaiwen Sun
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.17676
UR  - https://arxiv.org/abs/2610.17676
AB  - We study certain simple affine vertex algebras L_−1−h/6(g) from rank-one Argyres-Douglas theories, where g is a non-simply-laced simple Lie algebra and h is its Coxeter number. For L_−3(F_4), we determine the maximal ideal of V^−3(F_4), Zhu's algebra, and the associated variety. We also classify the irreducible highest-weight L_−3(F_4)-modules and determine the characters of its irreducible ordinary modules. The associated variety is 𝕆̅_Ã_1, and the level −3 is totally collapsing for the orbit 𝕆_Ã_1. The Poisson coinvariants of the C_2-algebra of L_−3(F_4) are isomorphic to ℂ[ℓ]/(ℓ^5), where ℓ is induced by the conformal vector. Consequently, the characters of ordinary L_−3(F_4)-modules satisfy a fifth-order modular linear differential equation. We also give modular linear differential equations of orders five and eleven satisfied by the characters of ordinary modules for L_−2(B_3) and L_−2(G_2) respectively.
ER  -