Monte-Carlo simulation of the Gaussian BFSS matrix model at large number of dimensions

TL;DR

This thesis uses Monte Carlo simulations to study a Gaussian approximation of the bosonic BFSS matrix model, accurately reproducing the stringy phase transition and exploring matrix geometry and phase behavior at large dimensions.

Contribution

It introduces a Monte Carlo approach to analyze the Gaussian bosonic BFSS matrix model and investigates phase transitions and geometric configurations at large N.

Findings

Reproduced the Hagedorn phase transition with high accuracy.

Identified a crossover to a Wigner semi-circle law at small gauge coupling.

Observed the absence of uniform distribution at small temperatures.

Abstract

In this thesis, we studied a Gaussian approximation to the bosonic part of the BFSS matrix model using Monte Carlo simulations based on the Metropolis algorithm. We reproduce with great accuracy the stringy Hagedorn phase transition from a confinement (black string) phase to a deconfinement (black hole) phase. We used the Polyakov loop as an order parameter to investigate the large-N behavior of this model at different temperatures, other observables such as internal energy and extent of space were also computed. In the last part, we present the matrix-geometry approach to a modified action where we captured only a remnant of the geometric Yang-Mills to a baby-fuzzy-sphere phase where the fuzzy sphere solution is only manifested as a three-cut configuration. The Yang-Mills phase retains most of its characteristics with two exceptions: i) the uniform distribution inside a solid ball suffers a crossover at very small values of the gauge coupling constant to a Wigner's semi-circle law, and ii) the uniform distribution at small T is non-existent.