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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 $AdS_4times S^1times S^5$ solution of type IIB supergravity.
We construct supersymmetric solutions of $D=11$ supergravity, preserving 1/4 of the supersymmetry, that are holographically dual to ABJM theory which has been deformed by spatially varying mass terms depending on one of the two spatial directions. We
We find a family of complex saddle-points at large N of the matrix model for the superconformal index of SU(N) N=4 super Yang-Mills theory on $S^3 times S^1$ with one chemical potential $tau$. The saddle-point configurations are labelled by points $(
Superconformal indices (SCIs) of 4d ${mathcal N}=4$ SYM theories with simple gauge groups are described in terms of elliptic hypergeometric integrals. For $F_4, E_6, E_7, E_8$ gauge groups this yields first examples of integrals of such type. S-duali
We consider supergravity theories with 16 supercharges in Minkowski space with dimensions $d>3$. We argue that there is an upper bound on the number of massless modes in such theories depending on $d$. In particular we show that the rank of the gauge
We study supersymmetric sectors at half-BPS boundaries and interfaces in the 4d $mathcal{N}=4$ super Yang-Mills with the gauge group $G$, which are described by associative algebras equipped with twisted traces. Such data are in one-to-one correspond