$\mathcal{N}=2$ supersymmetric field theories on 3-manifolds with A-type boundaries

Abstract

General half-BPS A-type boundary conditions are formulated for N=2 supersymmetric field theories on compact 3-manifolds with boundary. We observe that under suitable conditions manifolds of the real A-type admitting two complex supersymmetries (related by charge conjugation) possess, besides a contact structure, a natural integrable toric foliation. A boundary, or a general co-dimension-1 defect, can be inserted along any leaf of this preferred foliation to produce manifolds with boundary that have the topology of a solid torus. We show that supersymmetric field theories on such manifolds can be endowed with half-BPS A-type boundary conditions. We specify the natural curved space generalization of the A-type projection of bulk supersymmetries and analyze the resulting A-type boundary conditions in generic 3d non-linear sigma models and YM/CS-matter theories.

66 pages

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• Localization of supersymmetric field theories on non-compact hyperbolic three-manifolds
• Superconformal Boundaries in $4-\epsilon$ dimensions
• Boundaries and supercurrent multiplets in 3D Landau-Ginzburg models
• The energy-momentum multiplet of supersymmetric defect field theories
• Web of Seiberg-like dualities for 3d $\mathcal{N}=2$ quivers
• Deconstructing Defects
• Singular BPS boundary conditions in $\mathcal{N}=(2,2)$ supersymmetric gauge theories