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

We propose that Argyres-Douglas theories of type Dp(SU(N)) and (Ap−1, AN−1) — both realizable as Type A class theories with irregular punctures — can be obtained via a sequence of mass deformations from a common ancestor: a class theory with only regular punctures. Building on our previous work, this result establishes that these theories ultimately originate from 6d 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 Dp(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 ancestor. We substantiate our general claims with several detailed examples that explicitly illustrate the deformation procedure.