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

TL;DR

This paper explores new features of Argyres-Douglas theories, including their conformal manifolds, Higgs branches, and three-dimensional reductions, introducing novel quiver gauge theories and mirror descriptions.

Contribution

It provides new insights into AD theories with irregular punctures, proposing explicit 3D mirror quivers and identifying previously unstudied quiver gauge theories.

Findings

Explicit 3D mirror theories for AD theories

New quiver gauge theories with unitary and special unitary groups

Descriptions of Higgs branches and conformal manifolds

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.