We find the holographic dual to the three classes of superconformal Janus interfaces in N = 4 SYM that preserve three-dimensional N = 4, N = 2, and N = 1 supersymmetry. The solutions are constructed in five-dimensional SO(6) maximal gauged supergravity and are then uplifted to type IIB supergravity. Corresponding to each of the three classes of Janus solutions, there are also AdS 4 × S 1 × S 5 J-fold backgrounds. These J-folds have a non-trivial SL(2, Z) monodromy for the axio-dilaton on the S 1 and are dual to three-dimensional superconformal field theories.

We show that for every Sasaki-Einstein manifold, M5, the AdS5 × M5 background of type IIB supergravity admits two universal deformations leading to supersymmetric AdS4 solutions. One class of solutions describes an AdS4 domain wall in AdS5 and is dual to a Janus configuration with N = 1 supersymmetry. The other class of backgrounds is of the form AdS4 × S 1 × M5 with a nontrivial SL(2, Z) monodromy for the IIB axio-dilaton along the S 1 . These AdS4 solutions are dual to three-dimensional N = 1 SCFTs. Using holography we express the S 3 free energy of these theories in terms of the conformal anomaly of the four-dimensional N = 1 SCFT arising from D3-branes on the Calabi-Yau cone over M5.

We employ a non-compact gauging of four-dimensional maximal supergravity to construct a two-parameter family of AdS4 J-fold solutions preserving $$ \mathcal{N} $$ N = 2 supersymmetry. All solutions preserve $$ \mathfrak{u} $$ u (1) × $$ \mathfrak{u} $$ u (1) global symmetry and in special limits we recover the previously known $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{u} $$ u (1) invariant $$ \mathcal{N} $$ N = 2 and $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{su} $$ su (2) invariant $$ \mathcal{N} $$ N = 4 J-fold solutions. This family of AdS4 backgrounds can be uplifted to type IIB string theory and is holographically dual to the conformal manifold of a class of three-dimensional S-fold SCFTs obtained from the $$ \mathcal{N} $$ N = 4 T [U(N)] theory of Gaiotto-Witten. We find the spectrum of supergravity excitations of the AdS4 solutions and use it to study how the operator spectrum of the three-dimensional SCFT depends on the exactly marginal couplings.

We find a new supersymmetric solution of type IIB supergravity which is holographically dual to the planar limit of the four-dimensional N = 2 * supersymmetric Yang-Mills theory on S 4 . We study a probe fundamental string in this background which is dual to a supersymmetric Wilson loop in the N = 2 * theory. Using holography we calculate the expectation value of this line operator to leading order in the 't Hooft coupling. The result is a non-trivial function of the mass parameter of the N = 2 * theory that precisely matches the result from supersymmetric localization.

The main ingredient for local superconformal methods is the multiplet of gauge fields: the Weyl multiplet. We construct the transformations of this multiplet for N = 3, D = 4. The construction is based on a supersymmetry truncation from the N = 4 Weyl multiplet, on coupling with a current multiplet, and on the implementation of a soft algebra at the nonlinear level, extending su(2, 2|3). This is the first step towards a superconformal calculus for N = 3, D = 4.