Bootstrap to Gravity

TL;DR

This review discusses using the bootstrap method, especially matrix bootstrap, to precisely analyze high energy and holographic models, offering an alternative to Monte Carlo methods and extending to dynamical scenarios.

Contribution

It introduces a matrix bootstrap approach that achieves high-precision solutions for complex models in high energy theory and holography, surpassing traditional numerical methods.

Findings

Matrix bootstrap determines solution ranges with exponential precision increase.

Applicable to models like BFSS MQM, D-instanton/IKKT, and BMN theory.

Extends to thermal and time-dependent cases for dynamical analysis.

Abstract

In this review, we aim to utilize the bootstrap method to study models that have received significant interest in high energy theory and holography recently. Matrix bootstrap is proposed to determine the range of the solution up to an impressively high precision merely through positive conditions rooted in fundamental quantum mechanical structures or reality of matrix integral saddle points, together with specific kinematical and dynamical constraints of the theory, whose precision increases exponentially with the number of variables taken into consideration in principle. It plays the role of an equivalently effective substitute for the numerical Monte Carlo method. Models that could potentially be explored with this approach include BFSS MQM (conjectured to be the first non-perturbative definition of M theory in 11d and dual to D0 brane black hole solutions in 10d supergravity), D-instanton/IKKT matrix integral (which has recently attracted particular attention for its relations with spacetime emergence) and mass deformed BMN theory. Apart from exploring the stationary state properties of the theory, we can extend the method to thermal or time-dependent cases to study the dynamical information of the properties and help to verify or predict the possibility of holographic realization in these models.