Anatomy of bubbling solutions

TL;DR

This work develops a precise holographic framework to extract vevs from bubbling LLM geometries in AdS5×S5 and demonstrates that the LLM 2D droplet density fixes all single-trace 1/2-BPS operator vevs at leading order in N, matching field theory results up to dimension four. Using KK holography, the authors connect 10D bubbling data to 5D fields and compute holographic vevs for the stress tensor, R-currents, and chiral primaries, confirming exact agreement with N=4 SYM expectations and Coulomb-branch limits. They also clarify the state-density correspondence: while the droplet distribution encodes single-trace data, it generally does not determine the full quantum state, requiring multi-trace information to resolve degeneracies, and they reveal a coherent-state interpretation for ripple-like deformations. The analysis draws deep connections between supergravity, free fermions, and collective chiral boson descriptions, offering a holographic blueprint for reconstructing bulk geometries from boundary data and highlighting the role of higher-point correlators in distinguishing microstates.

Abstract

We present a comprehensive analysis of holography for the bubbling solutions of Lin-Lunin-Maldacena. These solutions are uniquely determined by a coloring of a 2-plane, which was argued to correspond to the phase space of free fermions. We show that in general this phase space distribution does not determine fully the 1/2 BPS state of N=4 SYM that the gravitational solution is dual to, but it does determine it enough so that vevs of all single trace 1/2 BPS operators in that state are uniquely determined to leading order in the large N limit. These are precisely the vevs encoded in the asymptotics of the LLM solutions. We extract these vevs for operators up to dimension 4 using holographic renormalization and KK holography and show exact agreement with the field theory expressions.

Figures (6)

• Figure 1: Sharpened distributions describing Schur polynomials of the same dimension $n \ll N$ cannot be distinguished by the corresponding vevs at leading order in $N$.
• Figure 2: Distribution for a typical Schur polynomial; there is no distinct peak. The figure shows $N=100$, $n=30$, with a random distribution of $\lambda_p$.
• Figure 3: Distribution for a Schur polynomial in which the $\lambda_p$ are equal. The figure shows $N=120$, $n=30$ with $\lambda_p =2$ for $p \le 15$.
• Figure 4: A maximal giant graviton corresponds to a disc with a small hole at the centre.
• Figure 5: A disc plus droplet corresponds to a superposition of Schur polynomials of all dimension.