  We study mass deformations of $\mathcal{N}=4$, $d=4$ SYM theory that are
spatially modulated in one spatial dimension and preserve some residual
supersymmetry. We focus on generalisations of $\mathcal{N}=1^*$ theories and
show that it is also possible, for suitably chosen supersymmetric masses, to
preserve $d=3$ conformal symmetry associated with a co-dimension one interface.
Holographic solutions can be constructed using $D=5$ theories of gravity that
arise from consistent truncations of $SO(6)$ gauged supergravity and hence type
IIB supergravity. For the mass deformations that preserve $d=3$ superconformal
symmetry we construct a rich set of Janus solutions of $\mathcal{N}=4$ SYM
theory which have the same coupling constant on either side of the interface.
Limiting classes of these solutions give rise to RG interface solutions with
$\mathcal{N}=4$ SYM on one side of the interface and the Leigh-Strassler (LS)
SCFT on the other, and also to a Janus solution for the LS theory. Another
limiting solution is a new supersymmetric $AdS_4\times S^1\times S^5$ solution
of type IIB supergravity.
