Higgs branches of Argyres-Douglas theories as quiver varieties

Abstract

We present a general prescription for constructing 3d mathcal{N} = 4 Lagrangians for the IR SCFTs that arise from the circle reduction of a large class of Argyres-Douglas theories. The resultant Lagrangian gives a realization of the Higgs branch of the 4d SCFT as a quiver variety, up to a set of decoupled interacting SCFTs with empty Higgs branches. As representative examples, we focus on the families (Ap−N−1, AN−1) and Dp(SU(N)). The Lagrangian in question is generically a non-ADE-type quiver gauge theory involving only unitary gauge nodes with fundamental and bifundamental hypermultiplets, as well as hypermultiplets which are only charged under the U(1) subgroups of certain gauge nodes. Our starting point is the Lagrangian 3d mirror of the circle-reduced Argyres-Douglas theory, which can be read off from the class mathcal{S} construction. Using the toolkit of the S-type operations, developed in [1], we show that the mirror of the 3d mirror for any Argyres-Douglas theory in the aforementioned families is guaranteed to be a Lagrangian theory of the above type, up to some decoupled free sectors. We comment on the extension of this procedure to other families of Argyres-Douglas theories. In addition, for the case of Dp(SU(N)) theories, we compare these 3d Lagrangians to the ones found in [2] and propose that the two are related by an IR duality. We check the proposed IR duality at the level of the three-sphere partition function for specific examples. In contrast to the 3d Lagrangians in [2], which are linear chains involving unitary-special unitary nodes, we observe that the Coulomb branch global symmetries are manifest in the 3d Lagrangians that we find.