# Areas and entropies in BFSS/gravity duality

### Submission summary

 As Contributors: Tarek Anous · Joanna Karczmarek Arxiv Link: https://arxiv.org/abs/1911.11145v2 (pdf) Date accepted: 2020-04-09 Date submitted: 2020-04-07 02:00 Submitted by: Anous, Tarek Submitted to: SciPost Physics Academic field: Physics Specialties: High-Energy Physics - Theory Quantum Physics Approach: Theoretical

### 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.

### Ontology / Topics

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Published as SciPost Phys. 8, 057 (2020)

Dear Editor,

We have made revisions to the paper that address the points of the
referee.

### List of changes

subsections of section 6 emphasizing that understanding entropies in the
BFSS model is challenging, both because there are no spatial subsystems
(in contrast to higher-dimensional examples of AdS/CFT) and because the
model is gauged. We also made it more clear that the obvious tensor
factors present in the ungauged model are not necessarily the right
subsystems to associate with the bulk extremal surfaces.

For point 2), we have moved the pedagogical examples of entropy
calculations for simple systems to appendix A.