Supersymmetric Chern-Simons Theory in Presence of a Boundary

TL;DR

This paper develops a supersymmetric and gauge-invariant formulation of Chern-Simons theory with boundaries by adding boundary degrees of freedom, and applies it to the ABJM model, ensuring consistent symmetries.

Contribution

It introduces a boundary-compatible supersymmetric and gauge-invariant Chern-Simons theory, extending to the ABJM model with BRST symmetries.

Findings

Supersymmetric boundary conditions are established.

Gauge invariance is restored via boundary degrees of freedom.

BRST and anti-BRST symmetries are formulated for the boundary theory.

Abstract

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.