Abstract
The BFSS matrix model provides an example of gauge-theory / gravity duality where the gauge theory is a model of ordinary quantum mechanics with no spatial subsystems. If there exists a general connection between areas and entropies in this model similar to the Ryu-Takayanagi formula, the entropies must be more general than the usual subsystem entanglement entropies. In this note, we first investigate the extremal surfaces in the geometries dual to the BFSS model at zero and finite temperature. We describe a method to associate regulated areas to these surfaces and calculate the areas explicitly for a family of surfaces preserving SO(8) symmetry, both at zero and finite temperature. We then discuss possible entropic quantities in the matrix model that could be dual to these regulated areas.
Highlights
2.1 The BFSS modelThe BFSS matrix model is a quantum mechanical system defined by the Hamiltonian H = tr − g 2 Y M [X i, X j ]2 +gY M Ψαγαi β [X i, Ψβ ] (1)together with the constraint that the states should be invariant under the U(N ) symmetry of the model
In the context of the AdS/CFT correspondence, this is manifested most clearly in the Ryu-Takayanagi formula [2,6] that relates the areas of extremal surfaces in the gravity picture to the entanglement entropy of spatial subsystems in the dual CFT
We focus on the surfaces with ball topology and define a regulated area for these surfaces. We numerically compute this area as a function of mimimum radial coordinate for surfaces in the vacuum geometry and the black hole geometries dual to thermal states
Summary
There is increasing evidence that spacetime geometry is related in a fundamental way to the entanglement structure of the underlying degrees of freedom in quantum theories of gravity [1,2,3,4,5]. In the context of the AdS/CFT correspondence, this is manifested most clearly in the Ryu-Takayanagi formula [2,6] that relates the areas of extremal surfaces in the gravity picture to the entanglement entropy of spatial subsystems in the dual CFT. We will focus on gravitational observables that are localized to the region in which classical gravity provides a good description We consider both the vacuum state of the model and finite temperature states, dual to tendimensional D0-brane black holes. We numerically compute this area as a function of mimimum radial coordinate for surfaces in the vacuum geometry and the black hole geometries dual to thermal states.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
