Abstract
Mirror symmetry, a three dimensional mathcal{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 S2 × S1. 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 mathcal{N} = 4 Lagrangians for 3d SCFTs, which arise in the deep IR limit of certain Argyres-Douglas theories compactified on a circle.
Highlights
In spite of the impressive success of perturbative QFT, the study of nonperturbative/strongly coupled aspects of a QFT remains a challenge for theorists
We explicitly realize this program in terms of two RG-invariant supersymmetric observables — the S3 partition function and the S2 × S1 superconformal index, which can be computed using localization techniques
Consider a pair of dual quiver gauge theories (X, Y ) where X is in class U, with a Higgs branch global symmetry subgroup Gsgulobbal = γ U(Mγ)
Summary
In spite of the impressive success of perturbative QFT, the study of nonperturbative/strongly coupled aspects of a QFT remains a challenge for theorists. For the purpose of this paper, we will choose the set of basic dualities as the set of good linear quivers [27] with unitary gauge groups, where the mirror symmetry (including the mirror map) is completely understood, both from String Theory and QFT With this choice of the pair (X, Y ), the construction of figure 1 can be seamlessly implemented to generate a new dual pair (X , Y ). These two subsections contain the main results of this paper in terms of constructing new mirror dualities.
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