Emergent geometry through quantum entanglement in Matrix theories

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.

Automated summary

The study reveals a direct link between the entanglement entropy of a probe giant graviton and the local tidal acceleration experienced by the probe in a specific theoretical framework, establishing a new connection between local spacetime geometry and quantum entanglement. Expanding this theory to different backgrounds, a new relationship is conjectured between entanglement in Matrix theories and local spacetime geometry. This relationship involves a 'c-tensor' measuring the evolution of local transverse area and its connection to the local energy-momentum tensor measured by a probe.