geometry, with direct extensions to cylindrical and spherical geometries. Janus field theories were motivated, from the gravitational sector of the AdS/CFT correspondence, by an exact and non-singular solution for the dilatonic field in type II-B supergravity, which was found in a simple deformation of the $AdS_{5}\times S^{5}$ geometry [@Bak]. Even though the solution breaks all the original supersymmetries it proves to be stable under a large class of perturbations [@Bak; @FNSS; @CCDAVPZ]. The dilaton acquires a constant value at the boundary, where $AdS_{5}$ is recovered, but adopts different values at each half of the boundary. On the other hand, the AdS/CFT correspondence requires the existence of a dual gauge theory on the boundary for every non-singular solution of type IIB supergravity with appropriate asymptotics which in this case is a four dimensional $\mathcal{N}=4$ SYM theory living in the boundary [@Bak]. In other words, a running dilaton induces space-time dependent coupling constants in the gauge theories in the dual sector, which defines what is called a Janus field theory. In our case, the four dimensional $\mathcal{N}=4$ SYM theory is replaced by the CS modified ED, where we take the electromagnetic coupling to be globally constant, while the topological coupling to the 