Abelian dualities of $\mathcal{N}=(0,4)$ boundary conditions

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 't 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.

arXiv comment81 pages, 17 figures, v3: published version

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• BFT${}_2$: a General Class of $2d$ $\mathcal{N}=(0,2)$ Theories, 3-Manifolds and Toric Geometry
• Orbifold ETW brane and half-indices
• Boundary confining dualities and Askey-Wilson type $q$-beta integrals
• 3d exceptional gauge theories and boundary confinement
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• Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs
• Abelian dualities and line defect indices for 3d gauge theories
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• $SL(2,\mathbb{Z})$ dualities of boundary conditions in Abelian M2-brane SCFTs