Target space entanglement in a matrix model for the bubbling geometry

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 $Ad{S}_5\times S^5$, 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.

arXiv comment19 pages, 16 figures, published version

References in corpus (12)

• Gauge Theory Correlators from Non-Critical String Theory
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• M Theory As A Matrix Model: A Conjecture
• Bubbling AdS space and 1/2 BPS geometries
• A toy model for the AdS/CFT correspondence
• The entanglement entropy of one-dimensional gases
• Entanglement entropy of integer Quantum Hall states
• LLL vs. LLM: Half BPS Sector of N=4 SYM Equals to Quantum Hall System
• Complex Matrix Model and Fermion Phase Space for Bubbling AdS Geometries
• Gauge Invariant Target Space Entanglement in D-Brane Holography
• Bulk Entanglement Entropy and Matrices
• Target space entanglement in quantum mechanics of fermions and matrices

Cited by in corpus (4)

• Entanglement Entropy and Phase Space Density: Lowest Landau Levels and 1/2 BPS states
• Target Space Entanglement in Quantum Mechanics of Fermions and Matrices
• Target space entanglement in quantum mechanics of fermions at finite temperature
• Ensemble averaging in JT gravity from entanglement in Matrix Quantum Mechanics