ABJM Mirrors and a Duality of Dualities

TL;DR

The paper investigates how mirror symmetry acts on three-dimensional CS-matter theories with varying supersymmetry, building a comprehensive network of dualities through IIB brane constructions, SL(2,Z) transformations, and brane webs. It introduces geometric duality via M-theory, showing that different IIA/IIB realizations correspond to the same CY4 geometry and IR fixed point, and it connects toric duality with Seiberg duality under this duality map. Key results include new CS-mirror pairs, ABJM-like constructions with (1,1) branes, and a unifying AdS/CFT framework for M2 branes on toric CY singularities. The work provides a unified perspective on how various dualities—mirror symmetry, Seiberg duality, and toric duality—are different facets of a single M-theory description, with concrete geometric and brane-theoretic realizations.

Abstract

We clarify how mirror symmetry acts on 3d theories with N=2,3 or 4 supersymmetries and non-abelian Chern-Simons terms and then construct many new examples. We identify a new duality, geometric duality, that allows us to generate large families of gauge theories, with and without Chern-Simons term, that all flow to the same conformal field theory in the infrared. In particular, we find an interesting duality of dualities: a pair of theories related via mirror symmetry can be mapped, via geometric duality, into a pair of gauge theories related by Seiberg duality. This network of dualities can be understood as the simple result that all of these theories are different realizations of one and the same system in M-theory.