Higgs branches of Argyres-Douglas theories as quiver varieties

We present a general prescription for constructing 3dN= 4Lagrangiansfor the IR SCFTs that arise from the circle reduction of a large class of Argyres-Douglastheories. The resultant Lagrangian gives a realization of the Higgs branch of the 4d SCFTas a quiver variety, up to a set of decoupled interacting SCFTs with empty Higgs branches.As representative examples, we focus on the families(A(p-N-1),A(N-1))andD(p)(SU(N)).The Lagrangian in question is generically a non-ADE-type quiver gauge theory involvingonly unitary gauge nodes with fundamental and bifundamental hypermultiplets, as wellas hypermultiplets which are only charged under theU(1)subgroups of certain gaugenodes. Our starting point is the Lagrangian 3d mirror of the circle-reduced Argyres-Douglas theory, which can be read off from the classSconstruction. Using the toolkit oftheS-type operations, developed in [1], we show that the mirror of the 3d mirror for anyArgyres-Douglas theory in the aforementioned families is guaranteed to be a Lagrangiantheory of the above type, up to some decoupled free sectors. We comment on the extensionof this procedure to other families of Argyres-Douglas theories. In addition, for the caseofD(p)(SU(N))theories, we compare these 3d Lagrangians to the ones found in [2] andpropose that the two are related by an IR duality. We check the proposed IR duality atthe level of the three-sphere partition function for specific examples. In contrast to the3d Lagrangians in [2], which are linear chains involving unitary-special unitary nodes, weobserve that the Coulomb branch global symmetries are manifest in the 3d Lagrangiansthat we find