The Conformal Manifold of S-folds in String Theory

We continue the holographic exploration of the conformal manifold of 3d $\mathcal{N}=2$ S-fold SCFTs constructed by gauging the flavor symmetry of the Gaiotto-Witten $T[U(N)]$ theory. We show how to uplift the two-parameter family of AdS$_4$ vacua dual to this conformal manifold to 10d backgrounds of type IIB supergravity. We use these uplifted solutions to shed new light on the mysterious nature of the infinite distance limit on the conformal manifold and to study probe strings and D3-branes. This analysis uncovers an intriguing structure of the $S^3$ partition function of the S-fold SCFTs which resembles the giant graviton expansion of the superconformal index of 4d $\mathcal{N}=4$ SYM. We also show how to each member of the family of supersymmetric AdS$_4$ vacua one can associate a consistent truncation to 4d $\mathcal{N}=2$ gauged supergravity and use this result, in conjunction with holography, to calculate the large $N$ partition function of the 3d S-fold SCFT on compact Euclidean manifolds. Finally, we generalize the supersymmetric AdS$_4$ vacua to a four-parameter family of non-supersymmetric AdS$_4$ solutions.