Non-perturbative Studies of Non-conformal Field Theories

Abstract

Many of the exciting features of the Standard Model of the elementary particles are inherently non-perturbative. A theoretical understanding of many physics aspects beyond the Standard Model of elementary particles also requires a non-perturbative framework. One such framework involves discretizing quantum field theories on a spacetime lattice. We can use this lattice regularization method to study supersymmetric versions of physics beyond the Standard Model. In this thesis, we discuss the spacetime lattice setup, and with the examples of different models, we will see the numerical capability of this tool in exploring field theory regimes that are not accessible through perturbation theory. We use an efficient version of the Monte Carlo algorithm to update the field configurations in the path integral and eventually reach the equilibrium configurations. A version of the gauge/gravity conjecture connects weakly coupled gravitational theories to strongly coupled field theories. We will mainly focus on the non-conformal analogs of the conjecture in lower dimensions. This thesis mainly discusses the numerical simulation results of two lower-dimensional models. One is the bosonic version of the BMN matrix quantum mechanics and the other is a two-dimensional Yang-Mills theory containing four supersymmetries. Our numerical results suggest that the phase diagram of bosonic BMN model smoothly interpolates between the bosonic BFSS and the gauged Gaussian model, with first-order deconfinement phase transition at all couplings. Our simulation results for two-dimensional Yang-Mills theory that contains four supersymmetries show that this model admits a deconfinement phase transition in the limit of a large number of colors. We also show that the nature of the transition looks similar to its maximally supersymmetric cousin in the weak coupling regime.