Three Dimensional Mirror Symmetry beyond $ADE$ quivers and Argyres-Douglas theories

TL;DR

This work extends 3d ${\cal N}=4$ mirror symmetry beyond ADE quivers by introducing a systematic framework of generalized ${\cal S}$-type operations, built from gauging, flavoring, identification, and defects, acting on dual pairs of A-type linear quivers. By leveraging RG-invariant observables—most notably the round ${\rm S^3}$ partition function and the ${\rm S^2\times S^1}$ superconformal index—the authors explicitly construct new mirror pairs, including infinite non-ADE families, and read off dual gauge content via partition-function and index formalisms. A key contribution is the Abelian sector: four Abelian ${\cal S}$-type operation families generating non-ADE mirrors, with proven Lagrangian duals for the duals and detailed examples (Families I–IV); they also connect these constructions to Argyres-Douglas theories compactified on a circle, proposing Lagrangian ${\cal N}=4$ mirrors for several class ${\cal S}$ AD theories. The framework broadens the landscape of 3d mirrors, offers concrete Lagrangian descriptions for IR fixed points, and provides a powerful bridge between 3d dualities and class ${\cal S}$ constructions, with potential extensions to non-Abelian operations and higher-rank dualities.

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 $SL(2,\mathbb{Z})$ 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 $S^2 \times S^1$. 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 $\mathcal{N}=4$ Lagrangians for 3d SCFTs, which arise in the deep IR limit of certain Argyres-Douglas theories compactified on a circle.

Figures (38)

• Figure 1: Generating new dual pairs using an elementary $S$-type operation.
• Figure 2: LHS: A quiver diagram representing the field content of a 3d ${\cal N}=4$ theory with gauge group $G=U(N_1) \times U(N_2) \times SU(N_3) \times SU(N_4)$, and fundamental/bifundamental matter. The various conventions are listed on the RHS. In a quiver diagram, we will refer to the circles as gauge nodes and the boxes as flavor nodes.
• Figure 3: A generic linear quiver with $L$ gauge nodes.
• Figure 4: The figure on the left shows the Type IIB brane construction for the linear quiver on the right. The red nodes represent D5 branes, the horizontal blue lines are D3 branes, and the vertical black lines represent NS5 branes.
• Figure 5: The figure on the left shows the Type IIB brane construction for the linear quiver on the right. The red nodes represent D5 branes, the horizontal blue lines are D3 branes, and the vertical black lines represent NS5 branes.