Amir Raz Final Defense

Abstract: Quantum field theory remains at the epicenter of both theoretical high energy and condensed matter physics. Given this, it is quite surprising that many diverse systems at very different scales can be studied using the same tools of quantum field theory. While quantum field theory has been incredibly successful in describing many universal properties of condensed matter systems as well as the standard model of particle physics, there are still many systems and phenomena that are difficult to study using conventional quantum field theory techniques. This is either because such systems don't seem to nicely fit into the standard paradigms of quantum field theory, or because the coupling between the various constituents is strong and so the conventional perturbative methods break down. This thesis focuses on two such systems from arising from the study condensed matter, fractonic systems and the fractional quantum Hall effect; with two overarching goals: trying to understand exactly how these exotic condensed matter systems fit into (or expand) the paradigms of quantum field theory,  and adapting techniques developed in the high energy community to investigate strongly interacting systems in condensed matter.