Line Defects in Three Dimensional Mirror Symmetry beyond ADE quivers

TL;DR

This paper extends the construction of vortex line defects and their mirror maps to complex 3d $ ext{N}=4$ quiver gauge theories beyond ADE types, including theories with multiple bifundamental hypermultiplets, revealing new dualities and defect correspondences.

Contribution

It provides a new prescription for constructing vortex defects in non-ADE quivers and explores their mirror maps, especially in theories with multiple bifundamental hypermultiplets and dual mirror pairs.

Findings

Constructed vortex defects in non-ADE quivers.

Mapped vortex defects to Wilson defects in mirror theories.

Identified dualities relating different mirror pairs.

Abstract

Understanding the map of line defects in a Quantum Field Theory under a given duality is generically a difficult problem. This paper is the second in a series which aims to address this question in the context of 3d $\mathcal{N}=4$ mirror symmetry. A general prescription for constructing vortex defects and their mirror maps in quiver gauge theories beyond the $A$-type was presented by the author in an earlier paper [arxiv:2103.01243], where specific examples involving $D$-type and affine $D$-type quivers were discussed. In this paper, we apply the aforementioned prescription to construct a family of vortex defects as coupled 3d-1d systems in quiver gauge theories beyond the $ADE$-type, and study their mirror maps. Specifically, we focus on a class of quiver gauge theories involving unitary gauge nodes with edge multiplicity greater than 1, i.e. two gauge nodes in these theories may be connected by multiple bifundamental hypermultiplets. Quiver gauge theories of this type arise as 3d mirrors of certain Argyres-Douglas theories compactified on a circle. Some of these quiver gauge theories are known to have a pair of 3d mirrors, which are themselves related by an IR duality, discussed recently in [arxiv:2109.07493]. For a concrete example where a pair of 3d mirrors do exist, we study how the vortex defects constructed using our prescription map to Wilson defects in each mirror theory.