  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. We study
super-Yang-Mills theories in presence of a boundary using these results.
Finally, we study the Born-Infeld action in presence of a boundary. We analyse
the boundary effects for the Born-Infeld action coupled to a background dilaton
and an axion field. We also analyse the boundary effects for an non-abelian
Born-Infeld action. We explicitly construct the actions for these systems in
presence of a boundary. This action preserves half of the original
supersymmetry.

High Energy Physics - Theory