Abstract
General half-BPS A-type boundary conditions are formulated for \( \mathcal{N} \) = 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.
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Aprile, F., Niarchos, V. \( \mathcal{N} \) =2 supersymmetric field theories on 3-manifolds with A-type boundaries. J. High Energ. Phys. 2016, 126 (2016). https://doi.org/10.1007/JHEP07(2016)126
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DOI: https://doi.org/10.1007/JHEP07(2016)126