New aspects of Argyres--Douglas theories and their dimensional reduction

TL;DR

The paper advances a unified framework for Argyres–Douglas theories engineered from A-type class S with irregular punctures, including a regular puncture, by analyzing conformal manifolds, Higgs-branch structure, and robust 3d reductions. It shows that circle reduction yields Lagrangian linear quivers with unitary and special-unitary nodes and introduces explicit 3d mirrors (magnetic quivers) capturing the 4d Higgs data, including non-higgsable sectors that become twisted hypermultiplets in 3d. A central result is a general construction of mirrors for D_p(SU(N)) and related I_{p-N,N} theories via complete graphs of U(1) nodes connected to a tail, with a calculable number of free hypermultiplets H_free, consistent with SUSY-enhancing RG flows. The work also extends to D_p^{N-1}(SU(N)) families (Type II punctures), providing parallel mirror recipes and symmetry analyses, thereby offering a comprehensive map between 4d AD SCFTs and their 3d lagrangian descriptions and magnetic quivers.

Abstract

Argyres-Douglas (AD) theories constitute an infinite class of superconformal field theories in four dimensions with a number of interesting properties. We study several new aspects of AD theories engineered in $A$-type class $\mathcal{S}$ with one irregular puncture of Type I or Type II and also a regular puncture. These include conformal manifolds, structures of the Higgs branch, as well as the three dimensional gauge theories coming from the reduction on a circle. The latter admit a description in terms of a linear quiver with unitary and special unitary gauge groups, along with a number of twisted hypermultiplets. The origin of these twisted hypermultiplets is explained from the four dimensional perspective. We also propose the three dimensional mirror theories for such linear quivers. These provide explicit descriptions of the magnetic quivers of all AD theories in question in terms of quiver diagrams with unitary gauge groups, together with a collection of free hypermultiplets. A number of quiver gauge theories presented in this paper are new and have not been studied elsewhere in the literature.