Target space entanglement in Matrix Models

Abstract

We study target space entanglement in gauged multi-matrix models as models of entanglement between groups of D-branes separated by a planar entangling surface, paying close attention to the implementation of gauge invariance. We open with a review of target space entanglement between identical particles, which shares some important features (specifically a gauged permutation symmetry) with our main problem. For our matrix models, we implement a gauge fixing well-adapted to the entangling surface. In this gauge, we map the matrix model problem to that of entanglement of a $U(1)$ gauge theory on a complete or all-to-all lattice. Matrix elements corresponding to open strings stretching across the entangling surface in the target space lead to interesting contributions to the entanglement entropy.

arXiv comment34 pages, 3 figures

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• Gauge Invariant Target Space Entanglement in D-Brane Holography
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• Entanglement in the Quantum Hall Matrix Model
• Matrix Entanglement
• Definitions of entwinement
• Finiteness of Entanglement Entropy in Collective Field Theory
• Entanglement Entropy in Internal Spaces and Ryu-Takayanagi Surfaces
• Entanglement Entropy and Phase Space Density: Lowest Landau Levels and 1/2 BPS states
• Target Space Entanglement in Quantum Mechanics of Fermions and Matrices
• Entanglement and mixed states of Young tableau states in gauge/gravity correspondence