Three dimensional mirror symmetry beyond ADE quivers and Argyres-Douglas theories

Mirror symmetry, a three dimensional N = 4 IR duality, has been studied in detail for quiver gauge theories of the ADE-type (as well as their affine versions) with unitary gauge groups. The A-type quivers (also known as linear quivers) and the associated mirror dualities have a particularly simple realization in terms of a Type IIB system of D3-D5-NS5-branes. In this paper, we present a systematic field theory prescription for constructing 3d mirror pairs beyond the ADE quiver gauge theories, starting from a dual pair of A-type quivers with unitary gauge groups. The construction involves a certain generalization of the S and the T operations, which arise in the context of the SL(2, Z) action on a 3d CFT with a U(1) 0-form global symmetry. We implement this construction in terms of two supersymmetric observables - the round sphere partition function and the superconformal index on S-2 x S-1. We discuss explicit examples of various (non-ADE) infinite families of mirror pairs that can be obtained in this fashion. In addition, we use the above construction to conjecture explicit 3d N = 4 Lagrangians for 3d SCFTs, which arise in the deep IR limit of certain Argyres-Douglas theories compactified on a circle.

Automated summary

Mirror symmetry in three-dimensional gauge theories involving ADE quivers has been extensively studied, and this paper presents a systematic field theory prescription for constructing 3d mirror pairs beyond the ADE quiver gauge theories. The construction involves a generalization of S and T operations in the context of SL(2, Z) action on a 3d CFT with a U(1) 0-form global symmetry. Various non-ADE infinite families of mirror pairs can be obtained using this construction. Additionally, 3d N = 4 Lagrangians for 3d SCFTs are conjectured based on this construction.