ABJM Mirrors and a Duality of Dualities

TL;DR

This paper explores how mirror symmetry acts on 3d supersymmetric theories with Chern-Simons terms, introduces a new geometric duality linking various gauge theories, and reveals a network of interconnected dualities unified in M-theory.

Contribution

It introduces a new geometric duality that generates families of gauge theories flowing to the same IR fixed point and links mirror, Seiberg, and geometric dualities in a unified framework.

Findings

Identified a new geometric duality connecting different gauge theories.

Showed that mirror and Seiberg dualities are related via geometric duality.

Unified various dualities as different realizations of the same M-theory system.

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.