Exact Results in Supersymmetric Field Theories on Manifolds with Boundaries

TL;DR

This paper develops supersymmetric gauge theories on curved manifolds with boundaries, computes their partition functions and Wilson loops exactly using localization, and explores boundary conditions like Dirichlet.

Contribution

It introduces a method to construct and analyze supersymmetric theories on manifolds with boundaries, providing exact results for partition functions and Wilson loops.

Findings

Exact partition functions computed for theories on manifolds with boundaries.

Wilson loops evaluated precisely using localization techniques.

Boundary conditions like Dirichlet are effectively incorporated into supersymmetric theories.

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.