Gauge and Supersymmetry Invariance of N=2 Boundary Chern-Simons Theory

Abstract

In this paper, we study the restoration of gauge symmetry and up to half the supersymmetry (N=(2,0) or N=(1,1) in two dimensions) for N=2 non-Abelian Chern-Simons theories in the presence of a boundary. We describe the boundary action which is a supersymmetric WZW model coupled to the bulk Chern-Simons theory. Unlike the N=1 case, higher supersymmetry (N=(2,0)) will endow the group manifold of the WZW model with a complex structure. Therefore, the N=(2,0) WZW model in our paper is constructed via a coset space $G_c/G$, where $G$ is the same as the gauge group in the Chern-Simons action.

arXiv comment26 pages, accepted version. Corrected the arguments in pages 18-19, based on the anonymous referee's comments and improved the derivations in page 14

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• Singular BPS boundary conditions in $\mathcal{N}=(2,2)$ supersymmetric gauge theories
• 5d-4d Correspondence in Twisted M-theory on a Conifold
• $SL(2,\mathbb{Z})$ dualities of boundary conditions in Abelian M2-brane SCFTs