# Emergent spacetime & Quantum Entanglement in Matrix theory

## TL;DR

This paper explores how emergent spacetime and quantum entanglement manifest in Matrix theory, revealing non-commutative geometries and entanglement entropy related to black hole analogs and potential holographic dualities.

## Contribution

It demonstrates the emergence of non-commutative spacetime and entanglement entropy in Matrix theory, providing insights into flat space holography and black hole analogs.

## Key findings

- Membrane behaves like a smeared Matrix black hole
- Spacetime geometry can become non-commutative far from Planckian regions
- Entanglement entropy exists between supergravity modes and probes

## Abstract

In the context of the Bank-Fishler-Shenker-Susskind Matrix theory, we analyze a spherical membrane in light-cone M theory along with two asymptotically distant probes. In the appropriate energy regime, we find that the membrane behaves like a smeared Matrix black hole; and the spacetime geometry seen by the probes can become non-commutative even far away from regions of Planckian curvature. This arises from non-linear Matrix interactions where fast matrix modes lift a flat direction in the potential -- akin to the Paul trap phenomenon in atomic physics. In the regime where we do have a notion of emergent spacetime, we show that there is non-zero entanglement entropy between supergravity modes on the membrane and the probes. The computation can easily be generalized to other settings, and this can help develop a dictionary between entanglement entropy and local geometry -- similar to Ryu-Takayanagi but instead for asymptotically flat backgrounds.