Boundaries, mirror symmetry, and symplectic duality in 3d N=4 gauge theory

We introduce several families of N=2,2$$ \mathcal{N}=\left(2,\ 2\right) $$ UV boundary conditions in 3d N=4$$ \mathcal{N}=4 $$ gaugetheoriesandstudytheirIRimagesinsigma-modelstotheHiggsandCoulomb branches. In the presence of Omega deformations, a UV boundary condition defines a pair of modules for quantized algebras of chiral Higgs- and Coulomb-branch operators, respec-tively, whose structure we derive. In the case of abelian theories, we use …