Anatomy of bubbling solutions

TL;DR

This paper analyzes the holographic duals of LLM bubbling solutions, showing how phase space distributions determine vevs of 1/2 BPS operators in N=4 SYM and confirming their agreement with field theory calculations.

Contribution

It demonstrates that phase space distributions in LLM solutions determine vevs of 1/2 BPS operators, with explicit holographic calculations matching field theory results.

Findings

Vevs of operators up to dimension 4 are extracted holographically.

Phase space distribution determines vevs to leading order in large N.

Exact agreement with field theory expressions is confirmed.

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.