Bootstrap bounds on D0-brane quantum mechanics

TL;DR

This paper derives bootstrap bounds on correlation functions in D0-brane quantum mechanics, extending previous bounds and providing new insights into the dual black hole geometry with results close to Monte Carlo simulations.

Contribution

It introduces simple bootstrap bounds on correlation functions that extend virial theorem bounds to finite energies and provide the first non-trivial bounds on certain observables.

Findings

Bounds are within a factor of 2 of Monte Carlo results.

Bounds suggest features of the dual black hole geometry.

First non-trivial bounds on 1Tr X^2 in this context.

Abstract

We derive simple bootstrap bounds on correlation functions of the BFSS matrix theory/D0-brane quantum mechanics. The result strengthens and extends Polchinski's virial theorem bound to finite energies and gives the first non-trivial bound on $\langle{\text{Tr}\, X^2\rangle}$. Despite their simplicity, the bounds hint at some features of the dual black hole geometry. Our best lower bounds are already a factor of $\sim 2$ from existing Monte Carlo results.