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

Abstract

Mirror symmetry, a three dimensional $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ N = 4 Lagrangians for 3d SCFTs, which arise in the deep IR limit of certain Argyres-Douglas theories compactified on a circle.

Line Defects in Three Dimensional Mirror Symmetry beyond ADE quivers

“…For the special case of n = 2p and l = p , the quiver X reproduces the complete graph quiver with three vertices and edge multiplicity p -the 3d mirror of the (A 2 , A 3p−1 ) AD theory reduced on a circle. The mirror theory Y was first found in [7], and discussed further in [2]. We find a concrete example of a vortex defect of the form described above and its mirror dual in this case, as shown below.…”

“…In a recent paper [1], the author presented a general procedure for constructing vortex defects in quiver gauge theories beyond the A-type and studying their maps under 3d mirror symmetry to Wilson defects. The construction involves a certain generalization of the S-operation of Witten [6], which was defined as an S-type operation in [7]. As discussed in [1], these S-type operations can be used to construct vortex defects and the associated mirror maps in a large class of non-linear quiver gauge theories, starting from the vortex defects in the A-type (linear) quivers.…”

“…The theory X is the 3d mirror associated with the circle reduction of the AD theory D 9 (SU (3)). The quiver Y is the U -mirror of X (as described above), which was first found in [7] and discussed further in [2].…”

Magnetic quivers and line defects -- On a duality between 3d N=4 unitary and orthosymplectic quivers

“…Understanding D3-D5-NS5 brane dynamics in Type IIB theory [29] is indispensable to study duality of 3d N = 4 theories. At the same time, exact results in 3d N = 4 theories uncover detailed information about brane systems in Type IIB theory [33,34,52,57]. In this section, we study 3d N = 4 mirror symmetry in the presence of an O-plane, including line operators, from this point of view.…”

Conformal Manifolds and 3d Mirrors of $(D_n,D_m)$ Theories

“…Following previous work (see e.g. [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]) our goal is to construct the 3d mirror theory in the case of local Calabi-Yau geometries described by hypersurface singularities in C 4 . More specifically, in this note we consider hypersurfaces given by the sum of two ADE singularities (usually referred to as (G, G ) models [40]), where both singularities are of type D.…”