Target space entanglement in Matrix Models

TL;DR

This paper investigates target space entanglement in gauged multi-matrix models, revealing how gauge invariance and open string contributions influence entanglement entropy between separated D-brane groups.

Contribution

It introduces a gauge fixing method tailored for entangling surfaces in matrix models and maps the problem to a U(1) gauge theory on an all-to-all lattice.

Findings

Open strings crossing the entangling surface affect entanglement entropy.

Gauge fixing simplifies the matrix model to a lattice gauge theory.

Target space entanglement shares features with particle entanglement under permutation symmetry.

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.