Complex Matrix Model and Fermion Phase Space for Bubbling AdS Geometries

TL;DR

This paper establishes a rigorous connection between droplet configurations in bubbling AdS geometries, a complex matrix model, and free fermion phase space, providing new insights into the AdS/CFT correspondence and dual giant graviton operators.

Contribution

It demonstrates an exact equivalence between a holomorphic sector of a complex matrix model and one-dimensional free fermions, linking droplet geometries to fermion phase space in AdS/CFT.

Findings

Holomorphic sector of the matrix model is equivalent to 1D free fermions.

Droplet configurations correspond to fermion phase space distributions.

Operators for dual giant gravitons map to droplet configurations.

Abstract

We study a relation between droplet configurations in the bubbling AdS geometries and a complex matrix model that describes the dynamics of a class of chiral primary operators in dual N=4 super Yang Mills (SYM). We show rigorously that a singlet holomorphic sector of the complex matrix model is equivalent to a holomorphic part of two-dimensional free fermions, and establish an exact correspondence between the singlet holomorphic sector of the complex matrix model and one-dimensional free fermions. Based on this correspondence, we find a relation of the singlet holomorphic operators of the complex matrix model to the Wigner phase space distribution. By using this relation and the AdS/CFT duality, we give a further evidence that the droplets in the bubbling AdS geometries are identified with those in the phase space of the one-dimensional fermions. We also show that the above correspondence actually maps the operators of N=4 SYM corresponding to the (dual) giant gravitons to the droplet configurations proposed in the literature.