Investigations of Supersymmetric Lattice Theories

In this dissertation I use lattice field theory methods to study supersymmetric quantum field theories. Supersymmetry is an additional symmetry that is compatible with the Coleman-Mandula theorem that has an important place in modern theoretical physics. It is used to study the structure of quantum field theories and is an ingredient in many models among other uses. Lattice field theory is a method for obtaining non-perturbative predictions for strongly interacting theory. The method involves discretising the theory by replacing the spacetime by a finite grid of discrete sites connected by links and defining the fields and interaction on this finite set of sites in a way such that the original theory is obtained in the limit of infinite grid with sites infinitesimally close together. The reduction from infinite degrees of freedom to finite number allows us to study such systems using high-performance computing. Lattice field theory has been an incredibly successful in studying quantum chromodynamics(QCD) and QCD-like theories. Using it to study supersymmetric theories has a long history however it hasn't had the same kind of success because the discretisation procedure breaks supersymmetry. This makes obtaining the original theory challenging. The major result presented here is the phase transition in 3d Maximally Supersymmetric Yang-Mills that is consistent with expectations coming from holographic considerations. Further to that, Creutz ratio were used to define and measure a running coupling for this theory as well as its 4-dimensional counterpart. While inconclusive, the results imply that using more sophisticated techniques might be promising. In addition, code developments were made in the publicly available software used for the above results and are announced in the text.