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Published August 2021 | Published + Accepted Version
Journal Article Open

Emergent geometry through quantum entanglement in Matrix theories

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.

Additional Information

© 2021 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: March 19, 2021; Revised: June 15, 2021; Accepted: July 29, 2021; Published: August 16, 2021. VS would like to thank the IPhT at Saclay for hosting him. This work was supported by NSF grant number PHY-0968726. We thank Adam Busis for participating in the initial stages of the BMN computation.

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Published - Gray2021_Article_EmergentGeometryThroughQuantum.pdf

Accepted Version - 2103.06941.pdf

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Additional details

Created:
August 20, 2023
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October 23, 2023