SYZ Mirrors in non-Abelian 3d 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.