On Emergent Geometry from Entanglement Entropy in Matrix theory

TL;DR

This paper introduces a method using Matrix theory to compute entanglement entropy between a supergravity probe and membrane modes, revealing how entanglement encodes local gravitational geometry.

Contribution

It presents a novel technique to calculate entanglement entropy in Matrix theory, linking quantum entanglement with emergent gravitational geometry.

Findings

Membrane stretching induces entanglement between modes.

Entanglement entropy encodes information about local geometry.

Method demonstrates how gravity emerges from quantum entanglement.

Abstract

Using Matrix theory, we propose a technique on how to compute the entangle- ment entropy between a supergravity probe and modes on a spherical membrane. We demonstrate that a membrane stretched between the probe and the sphere entangles these modes and can lead to an the entanglement entropy that encodes information about local gravitational geometry seen by the probe.