One-point functions in 2D and 4D SUSY Janus

We calculate the one-point functions of the marginal operator ${\mathcal{L}}^{\mathrm{\prime }}$ dual to the space-varying dilaton in 4D and 2D holographic Janus interfaces, extending results in arXiv:hep-th/0407073. We compare strongly-coupled supergravity and weakly-coupled CFT limits across $\mathcal{N}=0,1,2,4$ holographic Janus interfaces in 4D SYM, and $\mathcal{N}=0,4$ Janus interfaces for 2D D1-D5 CFT. Exact agreement between these regimes occurs only for the half-BPS interfaces in both 4D and 2D cases, while for other interfaces they agree to first order of the jump parameter. This result reinforces that exact weak/strong coupling matching for interface observables on supersymmetric (SUSY) conformal manifolds is exclusive to maximally SUSY interfaces.