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.
Highlights
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
Summary
Consider a point particle of mass m — to function as a probe to eleven-dimensional supergravity. We have (a) shifted the acceleration by the effect of the PP-wave background so that this quantity measures exclusively the tidal acceleration from the back-reaction of the source on the PP-wave background; and (b) APP is acceleration with respect to light-cone time, not proper time, as the dot represents derivative with respect to x+ This means that the expression in the parenthesis is already of order hμν or equivalently V. We can see that, for m = 0, ArPP Arm2/(p+) to leading order in V , where Ar is defined once again as the tidal acceleration due to the source only, but measured with respect to proper time. We can use all the relations for the point probe we presented and apply them to the membrane probe’s center of mass motion, with p+1 → p+ and xr1 → xr. The light-cone momentum of the source, p+2 , would only appear in the potential V
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