SYZ Mirrors in non-Abelian 3d Mirror Symmetry

TL;DR

This paper explores the SYZ mirror symmetry in non-Abelian 3d settings, establishing a connection between the mirror of a space with a group action and a Lagrangian subvariety in gauge theory Coulomb branches.

Contribution

It proves that the SYZ mirror of a space with a Hamiltonian group action defines a canonical Lagrangian subvariety in the Coulomb branch of 3d gauge theory, extending mirror symmetry understanding.

Findings

Identifies a canonical complex Lagrangian in Coulomb branches.

Connects SYZ mirror construction with 3d gauge theory.

Provides a new perspective on non-Abelian mirror symmetry.

Abstract

In the SYZ program, the mirror of $Y$ is the moduli space of Lagrangian branes in $Y$. When $Y$ is equipped with a Hamiltonian $G$-action, we prove that its mirror determines a canonical complex Lagrangian subvariety in the Coulomb branch of the 3d $\mathcal{N}=4$ pure $G$-gauge theory.