Exact Results in Supersymmetric Field Theories on Manifolds with Boundaries

Abstract

We construct supersymmetric gauge theories on some curved manifolds with boundaries. Our examples include a part of three-sphere and a part of two-sphere. We concentrate on Dirichlet boundary conditions. For these theories on the manifolds with the boundaries, we compute the partition functions and the Wilson loops exactly using the localization technique.

52 pages, typos corrected and references added

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