Argyres-Douglas Theories in Class S Without Irregularity

TL;DR

Twisted $A_{2n}$ class $ S$ theories with regular punctures are shown to realise a broad set of Argyres-Douglas type SCFTs, challenging the belief that irregular punctures are required for such spectra. The paper provides a thorough analysis of the five twisted $A_2$ trinions, computing their central charges, Macdonald indices, Higgs branch chiral rings, and associated VOAs, and identifies four of them with known AD or related theories. Interconnections among the twisted trinions are elucidated via partial Higgsing, and generalized $S$-duality frames are explored, including concrete dual descriptions for specific gauged setups. The work also outlines directions for extending to twisted $A_{2n}$ theories and probing Coulomb branch spectra, including potential $a$-type constraints that could generate half-integer dimensions, thereby enriching the AD landscape in class $ S$.

Abstract

We make a preliminary investigation into twisted $A_{2n}$ theories of class S. Contrary to a common piece of folklore, we establish that theories of this type realise a variety of models of Argyres-Douglas type while utilising only regular punctures. We present an in-depth analysis of all twisted $A_2$ trinion theories, analyse their interrelations via partial Higgsing, and discuss some of their generalised S-dualities.