Branes and Mirror Symmetry in N=2 Supersymmetric Gauge Theories in Three Dimensions

TL;DR

This paper constructs mirror pairs of N=2 supersymmetric gauge theories in three dimensions using brane configurations and SL(2,Z) symmetry, revealing how quantum and classical properties are exchanged under mirror symmetry.

Contribution

It introduces a method to realize mirror symmetry in 3D N=2 theories via brane setups and string dualities, elucidating the exchange of quantum and classical features.

Findings

Mirror map exchanges Higgs and Coulomb branches.

Quantum complex structures map to classical structures in the mirror.

Open D-string instantons generate N=2 superpotentials.

Abstract

We use brane configurations and SL(2,Z) symmetry of the type IIB string to construct mirror N=2 supersymmetric gauge theories in three dimensions. The mirror map exchanges Higgs and Coulomb branches, Fayet-Iliopoulos and mass parameters and U(1)R symmetries. Some quantities that are determined at the quantum level in one theory are determined at the classical level of the mirror. One such example is the complex structure of the Coulomb branch of one theory which is determined quantum mechanically. It is mapped to the complex structure of the Higgs branch of the mirror theory, which is determined classically. We study the generation of N=2 superpotentials by open D-string instantons in the brane configurations.