Emergent geometry through quantum entanglement in Matrix theories

TL;DR

This paper explores how quantum entanglement in Matrix theories relates to local spacetime geometry, proposing a new mechanism for emergent geometry from quantum entanglement in M-theory contexts.

Contribution

It introduces a novel connection between entanglement entropy and local spacetime geometry in Matrix theories, extending to flat space and proposing a general relation involving a c-tensor.

Findings

Entanglement entropy correlates with tidal acceleration in Matrix theory.

A new map between quantum entanglement and spacetime geometry is established.

Conjecture of a general relation involving a c-tensor and local energy-momentum.

Abstract

In the setting of the Berenstein-Maldacena-Nastase Matrix theory, dual to light-cone M-theory in a PP-wave background, we compute the Von Neumann entanglement entropy between a probe giant graviton and a source. We demonstrate that this entanglement entropy is directly and generally related to the local tidal acceleration experienced by the probe. This establishes a new map between local spacetime geometry and quantum entanglement, suggesting a mechanism through which geometry emerges from Matrix quantum mechanics. We extend this setting to light-cone M-theory in flat space, or the Banks-Fischler-Shenker-Susskind Matrix model, and we conjecture a new general relation between a certain measure of entanglement in Matrix theories and local spacetime geometry. The relation involves a `c-tensor' that measures the evolution of local transverse area and relates to the local energy-momentum tensor measured by a probe.