N=4 Super Yang-Mills Theories and Their Spaces of Vacua

I began work with Dr. Argyres in the spring of 2020 and have continued to work with him since then. The problem we focused on has to do with understanding the space of lowest energy states of N=4 Supersymmetric Yang-Mills theories. This class of theories are quantum field theories that are built out of an underlying Lie Group and Lie Algebra. They also contain artificial symmetries which are not observed in nature, but which allow us to get a much better hold on the predictions, or the dynamics, of the theory. Studying these theories will help physicists to better understand our true physical models of the world such as the standard model of particle physics.

Just recently, in the spring of 2022, Dr. Argyres and I released a paper alongside Dr. Mario Martone from King's College London. This paper is associated with this work, and contains an interesting calculation which illuminates a misunderstanding that many researchers in the field previously had. You can find the paper on the ArXiv here. You can also see a technical description of the problem in my senior thesis here. This thesis describes the relevant problem we worked on at a level that is one step down from the level that the paper is written at. Thus, it is appropriate for those with an undergraduate degree in physics or mathematics. Lastly, associated with my senior thesis is also a poster that you can see below.