Janus configurations, Chern-Simons couplings, and The θ-Angle in super Yang-Mills theory

We generalize the half-BPS Janus configuration of four-dimensional $$ \mathcal{N} = 4 $$ super Yang-Mills theory to allow the theta-angle, as well as the gauge coupling, to vary with position. We show that the existence of this generalization is closely related to the existence of novel three-dimensional Chern-Simons theories with $$ \mathcal{N} = 4 $$ supersymmetry. Another closely related problem, which we also elucidate, is the D3-NS5 system in the presence of a four-dimensional theta-angle.