Target space entanglement in a matrix model for the bubbling geometry

TL;DR

This paper investigates the target space entanglement entropy in a matrix model related to bubbling geometries in AdS/CFT, comparing matrix model calculations with geometric boundary areas, revealing qualitative agreement.

Contribution

It introduces a detailed analysis of target space entanglement in a complex matrix model linked to bubbling geometries, connecting eigenvalue distributions with geometric boundaries.

Findings

Target space entanglement entropy matches boundary area in bubbling geometries.

Eigenvalue droplet configurations correspond to specific geometric states.

Qualitative agreement found between matrix model and geometric calculations.

Abstract

We study the target space entanglement entropy in a complex matrix model that describes the chiral primary sector in $\mathcal{N}=4$ super Yang-Mills theory, which is associated with the bubbling AdS geometry. The target space for the matrix model is a two-dimensional plane where the eigenvalues of the complex matrix distribute. The eigenvalues are viewed as the position coordinates of fermions, and the eigenvalue distribution corresponds to a droplet formed by the fermions. The droplet is identified with one that specifies a boundary condition in the bubbling geometry. We consider states in the matrix model that correspond to $AdS_5\times S^5$, an AdS giant graviton and a giant graviton in the bubbling geometry. We calculate the target space entanglement entropy of a subregion for each of the states in the matrix model as well as the area of the boundary of the subregion in the bubbling geometry, and find a qualitative agreement between them.