Holography of quarter-BPS AdS bubbles

Abstract

We consider the quarter-BPS sector of the AdS$_5$/CFT$_4$ duality, and provide a precise matching between specific CFT states and supergravity geometries beyond the linearized approximation. In the bulk, we focus on AdS bubbles geometries that fit within a consistent truncation to five-dimensional gauged supergravity. We show that the BPS equations can be decoupled, and study the resulting geometries both perturbatively and numerically. Applying the holographic dictionary, we compute the expectation values of light chiral primaries in these backgrounds. This data allows us to determine the dual CFT state up to quadratic order in the fluctuations, and to provide non-trivial consistency checks of the result. The resulting state is expressed as a linear combination of half-BPS double-trace operators, and of the unique $[2,0,2]$ quarter-BPS operator of the theory. As an application, we compute three-point functions involving two quarter-BPS operators and a half-BPS operator in the supergravity regime, finding an explicit example of a correlator that differs from its free theory value and that is therefore not protected.