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arXiv · 2103.06941

Emergent geometry through quantum entanglement in Matrix theories

Cameron Gray·Vatche Sahakian·William Warfield
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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.

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Cameron Gray, Vatche Sahakian, William Warfield. 2021-03-11. Emergent geometry through quantum entanglement in Matrix theories. https://doi.org/10.1007/jhep08(2021)072

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