Simulations of Bosonic BMN Matrix Model

TL;DR

This thesis uses lattice Monte Carlo simulations to study the phase structure of bosonic BMN and BFSS matrix models, identifying phase transitions and constructing a phase diagram.

Contribution

It provides the first detailed phase diagram of the bosonic BMN matrix model using hybrid Monte Carlo simulations with various observables.

Findings

Identification of a Hagedorn/deconfinement phase transition

Construction of a parametrized phase diagram

Validation of simulation algorithms with toy models

Abstract

In this thesis we provide the results obtained through lattice Monte Carlo simulations of the bosonic BMN and the bosonic BFSS matrix models. The simulations are performed using Hybrid Monte Carlo (HMC) algorithm. The BMN matrix model is expected to have a Hagedorn/deconfinement type phase transition as the temperature is varied in the system. The Polyakov loop is used as an order parameter for detecting the phase transition. Besides the Polyakov loop, other prime observables such as the internal energy and the extent of space were also computed. We also check the validity of numerical simulation algorithms by exploring the behavior of various relevant toy models. As the main result of this thesis, we present a parametrized phase diagram of the bosonic BMN matrix model constructed using two dimensionless parameters: a dimensionless coupling constant and a dimensionless temperature.