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.
Highlights
The study of supersymmetric quantum field theories on rigid curved backgrounds in diverse spacetime dimensions has been a powerful source of new non-perturbative results in recent years
We follow closely the conventions of ref. [3], where it was recognized that the existence of a supersymmetry implies a tranversely holomorphic foliation
The Reeb vector belongs to the foliation, and the algebra of supersymmetry is preserved on the leaves
Summary
The study of supersymmetric quantum field theories on rigid curved backgrounds in diverse spacetime dimensions has been a powerful source of new non-perturbative results in recent years. Our main motivation for the study of the classical problem in this paper is the eventual formulation of general half-BPS co-dimension-1 defects in 3d N = 2 supersymmetric quantum field theories on curved spaces, and the non-perturbative computation of observables associated with these defects. One can attempt to use the information of supersymmetric wavefunctions to study the structure of observables on closed manifolds that do not involve codimension-1 defects Hints of such a possibility come from a variety of previous results: the holomorphic block decomposition of 3d partition functions [19, 20], and the analogous phenomenon in different dimensions [7, 21, 22], the recent progress in computing D-brane.
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