### Four Dimensional Supersymmetric Theories in Presence of a Boundary

(0 votes over all institutions)

In this paper, we study $\mathcal{N} =1$ supersymmetric theories in four dimensions in presence of a boundary. We demonstrate that it is possible to preserve half the supersymmetry of the original theory by suitably modifying it in presence of a boundary. This is done by adding new boundary terms to the original action, such that the supersymmetric variation of the new terms exactly cancels the boundary terms generated by the supersymmetric transformation of the original bulk action. We also analyze the boundary projections of such supercharges used in such a theory. Finally, we study super-Yang-Mills theories in presence of a boundary using these results. We explicitly construct the action for the modified super-Yang-Mills theory, which preserves half the supersymmetry of the original theory, in presence of a boundary.