From Regular to Irregular: A Unified Origin for Argyres-Douglas Theories

TL;DR

This paper demonstrates that certain Argyres-Douglas theories can be derived from a common regular puncture theory through a sequence of mass deformations, revealing their origin from 6d theories and providing a constructive method using the Euclidean algorithm.

Contribution

It introduces a systematic, constructive approach to connect Argyres-Douglas theories to a regular puncture ancestor via mass deformations, utilizing the Euclidean algorithm and 3d mirror quivers.

Findings

Established a chain of deformations linking different $D_p(SU(N))$ theories.

Constructed a recursive method to build parent star-shaped quivers for any $(N,p)$.

Provided explicit examples illustrating the deformation procedure.

Abstract

We propose that Argyres-Douglas theories of type $D_p(\mathrm{SU}(N))$ 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 $D_p(\mathrm{SU}(N))$ 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.