Twisted A_2N Argyres--Douglas theories: vertex algebras, Higgs branches, and double covers

Abstract

We investigate the associated vertex operator algebras and Higgs branches of two closely related families of generalised Argyres--Douglas theories, arising from the twisted A_2N and twisted D_N+1 series, respectively. We propose that the A-series theories are realised as nilpotent Higgsings of the D-series, and we assemble a variety of pieces of evidence for this proposal. A consequence is that the associated vertex operator algebras of the A-series are finite extensions of affine Kac--Moody vertex algebras at (non-boundary) admissible levels, rather than those Kac--Moody algebras themselves, and that their Higgs branches are in many cases double covers of nilpotent orbit closures. The ℤ₂ gaugings of the A-series theories then furnish examples of unitary SCFTs whose associated vertex operator algebras are precisely affine Kac--Moody algebras at non-boundary admissible levels. We propose that these vertex algebras are equipped with a non-standard R-filtration, and comment on compatibility with graded unitarity.

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BibTeX RIS

BibTeX

@misc{beem2026twisted,
  title = {{Twisted $A_2N$ Argyres--Douglas theories: vertex algebras, Higgs branches, and double covers}},
  author = {Christopher Beem and Harshal Kulkarni},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25212},
  eprint = {2609.25212},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25212},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Twisted A_2N Argyres--Douglas theories: vertex algebras, Higgs branches, and double covers
AU  - Christopher Beem
AU  - Harshal Kulkarni
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.25212
UR  - https://arxiv.org/abs/2609.25212
AB  - We investigate the associated vertex operator algebras and Higgs branches of two closely related families of generalised Argyres--Douglas theories, arising from the twisted A_2N and twisted D_N+1 series, respectively. We propose that the A-series theories are realised as nilpotent Higgsings of the D-series, and we assemble a variety of pieces of evidence for this proposal. A consequence is that the associated vertex operator algebras of the A-series are finite extensions of affine Kac--Moody vertex algebras at (non-boundary) admissible levels, rather than those Kac--Moody algebras themselves, and that their Higgs branches are in many cases double covers of nilpotent orbit closures. The ℤ_2 gaugings of the A-series theories then furnish examples of unitary SCFTs whose associated vertex operator algebras are precisely affine Kac--Moody algebras at non-boundary admissible levels. We propose that these vertex algebras are equipped with a non-standard R-filtration, and comment on compatibility with graded unitarity.
ER  -

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