Twisted \texorpdfstring{$A_{2N}$}{A(2N)} Argyres--Douglas theories: vertex algebras, Higgs branches, and double covers

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 ${\mathbb{Z}}_2$ 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 $\mathfrak{R}$-filtration, and comment on compatibility with graded unitarity.