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

TL;DR

This paper investigates how gauge symmetry and partial supersymmetry are preserved in N=2 non-Abelian Chern-Simons theories with boundaries, introducing a boundary WZW model with complex structure for N=(2,0) cases.

Contribution

It constructs a boundary supersymmetric WZW model coupled to N=2 Chern-Simons theory, highlighting the role of complex structures in higher supersymmetry cases.

Findings

Boundary action as supersymmetric WZW model coupled to bulk Chern-Simons

N=(2,0) supersymmetry induces a complex structure on the WZW group manifold

Construction of the N=(2,0) WZW model via a coset space G_c/G

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.