## SciPost Submission Page

# Areas and entropies in BFSS/gravity duality

### by Tarek Anous, Joanna L. Karczmarek, Eric Mintun, Mark Van Raamsdonk, Benson Way

#### This is not the current version.

### Submission summary

As Contributors: | Tarek Anous · Joanna Karczmarek |

Arxiv Link: | https://arxiv.org/abs/1911.11145v1 (pdf) |

Date submitted: | 2020-01-28 01:00 |

Submitted by: | Anous, Tarek |

Submitted to: | SciPost Physics |

Discipline: | Physics |

Subject area: | High-Energy Physics - Theory |

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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### Submission & Refereeing History

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## Reports on this Submission

### Anonymous Report 1 on 2020-2-27 Invited Report

- Cite as: Anonymous, Report on arXiv:1911.11145v1, delivered 2020-02-27, doi: 10.21468/SciPost.Report.1541

### Strengths

1) Addresses an important outstanding question in holography by considering how entanglement of non-geometric degrees of freedom relates to geometry of gravitational theory.

2) Gives concrete proposals as to how the Ryu-Takayanagi formula might generalize to the BFSS matrix model despite lack of spatial subsystems.

3) Explicitly computes (regulated) areas of extremal surfaces preserving SO(8) symmetry in black brane background which should be dual to entropies in BFSS.

### Weaknesses

1) I am confused by the emphasis placed on the gauging of the BFSS matrix model at the beginning of section 6. First off, while it is true that the U(N) singlet constraint prevents a tensor factorization of the physical Hilbert space over matrix entries, it is not clear that would have been the desired factorization relevant for spatial subregions in the bulk (i.e. the subset of operators which can then reconstruct the dual operates within the "entanglement wedge"). Secondly, the contrast with N=4 SYM seems a bit surprising, since N=4 SYM is also a gauge theory with a physical Hilbert space that doesn't spatially tensor factorize (even for a lattice regularization). Further, it is unclear the algebras proposed later in that section don't have non-trivial centers (which, in the gauge theory case, is equivalent to the lack of simple tensor factorization).

2) Section 6 could have perhaps been streamlined. While the pedagogical presentation of entropies associated to subalgebras might be useful, the one qubit examples are possibly worked out in excessive detail for how relevant they are.

### Report

This paper makes concrete and original efforts to address a very important problem in holography, providing a step forward in generalizing RT to other string-based examples. While obviously very hard to compute in BFSS, it would be nice to find some testing ground for this proposal (perhaps in some simpler model), since many of the conjectures rely primarily on matching symmetries. Nonetheless, it is a precise and useful proposal relying on the parametrization of asymptotic data needed to specify these extremal surfaces.