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

Abstract

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.