Mirror Symmetry in Three-Dimensional Gauge Theories, Quivers and D-branes

TL;DR

This paper constructs and analyzes dual N=4 supersymmetric 3D gauge theories with unitary and symplectic groups, revealing mirror symmetry relations between their Coulomb and Higgs branches, and connecting these to string theory via D-branes and T-duality.

Contribution

It provides a detailed construction of mirror dualities for 3D N=4 theories with new explicit mirror maps and extends the understanding of moduli spaces in string theory contexts.

Findings

Mirror symmetry exchanges Coulomb and Higgs branches.

Explicit mirror maps relate mass and Fayet-Iliopoulos parameters.

Connections to ALE spaces and instanton moduli spaces.

Abstract

We construct and analyze dual N=4 supersymmetric gauge theories in three dimensions with unitary and symplectic gauge groups. The gauge groups and the field content of the theories are encoded in quiver diagrams. The duality exchanges the Coulomb and Higgs branches and the Fayet-Iliopoulos and mass parameters. We analyze the classical and the quantum moduli spaces of the theories and construct an explicit mirror map between the mass parameters and the the Fayet-Iliopoulos parameters of the dual. The results generalize the relation between ALE spaces and moduli spaces of SU(n) and SO(2n) instantons. We interpret some of these results from the string theory viewpoint, for SU(n) by analyzing T-duality and extremal transitions in type II string compactifications, for SO(2n) by using D-branes as probes. Finally, we make a proposal for the moduli space of vacua of these theories in the absence of matter.