Bulk Entanglement Entropy and Matrices

Abstract

Motivated by the Bekenstein Hawking formula and the area law behaviour of entanglement entropy, we propose that in any UV finite theory of quantum gravity with a smooth spacetime, the total entropy for a pure state in a co-dimension one spatial region, to leading order, is given by $S=\frac{A}{4G_N}$, where $A$ is the area of the co-dimension two boundary. In the context of $Dp$ brane holography we show that for some specially chosen regions bulk entanglement can be mapped to ``target space" entanglement in the boundary theory. Our conjecture then leads to a precise proposal for target space entanglement in the boundary theory at strong coupling and large $N$. In particular it leads to the conclusion that the target space entanglement would scale like $O(N^2)$ which is quite plausible in a system with $O(N^2)$ degrees of freedom. Recent numerical advances in studying the D0 brane system hold out the hope that this proposal can be tested in a precise way in the future.

Submitted 11 March 2020 to the Peter Freund Memorial Volume. J Phys A

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• Entanglement in the Quantum Hall Matrix Model
• Matrix Entanglement
• Target space entanglement in quantum mechanics of fermions and matrices
• Definitions of entwinement
• Entanglement Entropy in Internal Spaces and Ryu-Takayanagi Surfaces
• Quantum Entanglement on Black Hole Horizons in String Theory and Holography
• Finiteness of Entanglement Entropy in Collective Field Theory
• Minimal Areas from Entangled Matrices
• Emergent Area Laws from Entangled Matrices
• Target space entanglement in a matrix model for the bubbling geometry
• Large N Optimization for multi-matrix systems
• Entanglement Entropy and Phase Space Density: Lowest Landau Levels and 1/2 BPS states
• Target space entanglement in quantum mechanics of fermions at finite temperature