Monte Carlo Simulations of BFSS and IKKT Matrix Models

TL;DR

This thesis uses Monte Carlo simulations to analyze bosonic BFSS and IKKT matrix models, confirming phase transitions and symmetry properties, and validating simulation methods with toy models.

Contribution

It applies Hamiltonian Monte Carlo to study large-N behavior, phase transitions, and symmetry breaking in bosonic matrix models, providing new insights and validation of numerical techniques.

Findings

BFSS model exhibits a confinement-deconfinement phase transition.

No spontaneous symmetry breaking of SO(10) in the IKKT model.

Validated Monte Carlo methods with toy models.

Abstract

In this thesis, we studied the bosonic BFSS and IKKT matrix models using Monte Carlo simulations. First, we explored some toy models to check the validity of the numerical simulations. Then we simulated the BFSS matrix model using Hamiltonian Monte Carlo (HMC) algorithm. In the BFSS matrix model, we used the Polyakov loop as an order parameter to investigate the large-N behaviour of this model at different temperatures. Our simulations confirmed that the model exhibits a confinement-deconfinement phase transition as the temperature of the system is varied. Besides the Polyakov loop, other observables such as internal energy and extent of space were also computed. In the bosonic IKKT model, we studied the spontaneous symmetry breaking (SSB) of SO(10) symmetry using the moment of inertia tensor and found that there is no SSB of SO(10) symmetry in this model. Besides the eigenvalues of the moment of inertia tensor, other observable such as extent of spacetime was also computed. We also studied the simulation theory of the phase-quenched IKKT model.