Holography of quarter-BPS AdS bubbles

TL;DR

This work establishes a concrete non-linear holographic dictionary for quarter-BPS AdS bubbles in AdS$_5$/CFT$_4$ by employing a five-dimensional consistent truncation and a decoupled BPS framework to obtain perturbative and numerical bulk solutions. Using KK holography, it extracts dimension-2 chiral primary vevs, R-charges, and energy, and then constructs a perturbative heavy CFT state as a combination of the lightest quarter-BPS operator $O_{1/4}$ and relevant double-trace components, fixing coefficients through protected three-point functions. The main result is an explicit, finite-$N$ description of the dual state to the AdS bubble, including $1/N$ mixing with $O_{1/4}$ and a demonstration that protected quarter-BPS data are encoded in supergravity data alone, corroborated by numerical checks. This advances the microscopic understanding of quarter-BPS sectors in AdS$_5$/CFT$_4$ and provides a foundation for computing higher-point correlators in these backgrounds.

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.

Figures (6)

• Figure 1: Comparison between the full numerical solutions (solid blue lines) and the perturbative results at order 12 (dash-dotted red lines) for $\beta_1=\beta_2=1/10$. With these small values, the perturbation theory is a very good approximation of the real solutions.
• Figure 2: Comparison between the full numerical solutions (solid blue lines) and the perturbative results at order 12 (dash-dotted red lines) for $\beta_1=\beta_2=8/10$. At these values of the deformation parameters, the perturbation theory starts to deviate significantly from the numerical solutions.
• Figure 3: Energy, \ref{['eq:energy']}, of the solution, for equal $\beta_1=\beta_2$ with the full numerical result (blue hollow triangles) in comparison to the perturbative results at 12th order (red filled stars).
• Figure 4: The full numerical solutions for $\beta_1=\beta_2=2$. The perturbative results are not plotted, as they diverge too much from the numerical solutions for these large deformation parameters.
• Figure 5: Comparison between the full numerical solutions (solid blue lines) and the perturbative results (dash-dotted red lines) at order 12 for $\beta_1=1$ and $\beta_2=1/10$.