Abstract
We propose dual pairs of mathcal{N} = (0, 4) half-BPS boundary conditions for 3d mathcal{N} = 4 Abelian gauge theories related to mirror symmetry and S-duality by showing the matching of boundary ât Hooft anomalies and supersymmetric indices. We find simple mathcal{N} = (0, 4) mirror symmetry between 2d mathcal{N} = (0, 4) Abelian gauge theories and free Fermi multiplets that generalizes mathcal{N} = (0, 2) Abelian duality. We also propose a prescription for computing half-index of enriched Neumann boundary condition including 2d boundary bosonic matters by gauging the 2d boundary flavor symmetry of Dirichlet boundary condition. By coupling mathcal{N} = (0,4) half-BPS boundary configurations of 3d mathcal{N} = 4 gauge theories to quarter-BPS corner configurations of 4d mathcal{N} = 4 Super Yang-Mills theories, we further obtain a new type of 4d-3d-2d duality that may involve 3d non-Abelian gauge symmetry.
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