Areas and entropies in BFSS/gravity duality

TL;DR

This paper explores the relationship between areas and entropies in the BFSS matrix model's gravity dual, proposing a method to calculate extremal surface areas and discussing potential dual entropic quantities beyond standard entanglement entropy.

Contribution

It introduces a method to compute extremal surface areas in BFSS dual geometries and discusses their possible interpretation as generalized entropies in the matrix model.

Findings

Calculated extremal surface areas at zero and finite temperature.

Identified a family of symmetric surfaces for explicit area computation.

Discussed potential entropic quantities dual to these areas.

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.