From regular to irregular: a unified origin for Argyres-Douglas theories

A bstract We propose that Argyres-Douglas theories of type D p (SU( N )) and ( A p− 1 , A N− 1 ) — both realizable as Type A class $$\mathcal{S}$$ theories with irregular punctures — can be obtained via a sequence of mass deformations from a common ancestor: a class $$\mathcal{S}$$ theory with only regular punctures. Building on our previous work, this result establishes that these theories ultimately originate from 6d $$\mathcal{N}=(1, 0)$$ orbi-instanton theories compactified on a torus. The requisite 4d mass deformations are realized as tractable Fayet-Iliopoulos deformations on the 3d mirror quiver. The core of our method is a constructive procedure that utilizes the Euclidean algorithm to define a chain of deformations connecting different D p (SU( N )) theories. By reversing this chain, we recursively build a “parent” star-shaped quiver for any given ( N, p ). This quiver is the 3d mirror theory of the required class $$\mathcal{S}$$ ancestor. We substantiate our general claims with several detailed examples that explicitly illustrate the deformation procedure.