Line Defects in Three Dimensional Mirror Symmetry beyond ADE quivers

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 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 [1], 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 [2]. 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.

Line defects in three dimensional mirror symmetry beyond linear quivers

“…Type IIB realization. In a companion paper [8], we will apply our construction to study mirror maps of line defects in theories involving non-ADE quiver gauge theories.…”

“…Figure 8 gives an illustrative example of how one can read off the gauge theory content from the brane set up, using the rules listed above. Mirror symmetry in three dimensions can be understood as an S-duality of the above brane configuration, followed by a rotation R : x 7,8,9 → −x 4,5,6 , x 4,5,6 → x 7,8,9 . NS5 and D5 branes are exchanged under S-duality, while D3 branes are self-dual.…”

“…Given the Type IIB construction of the Wilson and the vortex defects in linear quivers, the mirror maps for such defects can be understood in the standard fashion. One implements an S-duality operation on a given brane configuration with defects, followed by a rotation x 7,8,9 → −x 4,5,6 , x 4,5,6 → x 7,8,9 , and finally a set of Hanany-Witten moves to read off the mirror theory with the dual defects. NS5 and NS5'-branes are exchanged with D5 and D5'-branes under S-duality, while D3-branes are self-dual, as before.…”

“…where W flavor i,q κ denotes a flavor Wilson defect with charge q κ for the U(1) i subgroup of the full flavor group, embedded as U(1) 1 ×U(1) 2 ×U(1) 3 ×U(1) 4 ⊂ SO (8). The charges (q κ 1 , q κ 2 ) are given by decomposing the representation R into U(1)…”

“…The U(1) flavor node identified with the 1d flavor symmetry in X[V r M,R ] is associated with the mass m 3 . 8 Following the general prescription of section 3.3, let us implement an S-type operation O P on the quiver X[V l 2,R ], where O P consists of a single gauging operation:…”