Holography of quarter-BPS AdS bubbles

TL;DR

This paper establishes a detailed holographic correspondence between specific quarter-BPS states in the AdS$_5$/CFT$_4$ duality and supergravity geometries, including subleading corrections, using both analytical and numerical methods.

Contribution

It provides a precise matching of CFT states with supergravity geometries beyond linear approximation, including quadratic order fluctuations and $1/N$ corrections.

Findings

Protected quarter-BPS operators are fully reconstructed from supergravity.

The BPS equations are decoupled and studied perturbatively and numerically.

The dual CFT states are expressed as linear combinations of half-BPS double-trace states.

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 a gauged five-dimensional supergravity. We show that the BPS equations can be decoupled, and we study the geometries 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. The resulting state is expressed as a linear combination of half-BPS double-trace states, and of the lightest quarter-BPS state of the theory. Our analysis reveals that protected quarter-BPS operators, including their subleading $1/N$ corrections, can be fully reconstructed from supergravity alone. Finally, we perform consistency checks of the result.