Supersymmetric Chern-Simons Theory in Presence of a Boundary

In this paper we analyse super-Chern-Simons theory in $\mathcal{N} =1$ superspace formalism, in the presence of a boundary. We modify the Lagrangian for the Chern-Simons theory in such a way that it is supersymmetric even in the presence of a boundary. Also, even though the Chern-Simons theory is not gauge invariant in the presence of a boundary, if it is suitable coupled to a gauged Wess-Zumino-Witten model, then the resultant theory can be made gauge invariant. Thus, by suitably adding extra boundary degrees of freedom, the gauge and supersymmetry variations of the boundary theory exactly cancel the boundary terms generated by the variations of the bulk Chern-Simons theory. We also discuss how this can be applied to the ABJM model in $\mathcal{N} =1$ superspace, and we then describe the BRST and anti-BRST symmetries of the resultant gauge invariant supersymmetric theory.