Mirror Symmetry and Toric Geometry in Three-Dimensional Gauge Theories

TL;DR

This paper explores three-dimensional N=2 supersymmetric gauge theories, demonstrating how Chern-Simons terms can compactify Coulomb branches and introducing a new class of mirror symmetric theories described via toric geometry.

Contribution

It introduces a novel class of mirror symmetric theories where both Coulomb and Higgs branches are characterized by toric geometry, linking gauge theory dynamics with geometric structures.

Findings

Coulomb branches can be made compact through Chern-Simons terms

New mirror symmetric theories with toric geometric descriptions

Both Coulomb and Higgs branches are described by toric geometry

Abstract

We study three dimensional gauge theories with N=2 supersymmetry. We show that the Coulomb branches of such theories may be rendered compact by the dynamical generation of Chern-Simons terms and present a new class of mirror symmetric theories in which both Coulomb and Higgs branches have a natural description in terms of toric geometry.