Gradient Flows in QCD-like Theories

One of the most important frameworks for understanding the fundamental interactions of elementary particles at the subatomic level is provided by non-Abelian gauge theories. They also feature in many hypothetical models that aim to further our understanding of nature beyond scales currently accessible by experiments. In this thesis we modify the short-distance behavior of these theories employing diffusion-like methods — specifically, gradient flows. Effectively, the elementary degrees-of-freedom are smeared over a region in spacetime, where the size of this region introduces a new scale into the system. By studying such smeared configurations we can gain insight into the workings of non-Abelian gauge theories. We specifically look at the impact of gradient flows on conservation laws that are linked to certain ‘flavor’ symmetries among quarks. In non-smeared systems these particular conservation laws are directly linked to a property known as nonrenormalization: an intricate cancellation occurs among divergent contributions, such that the final result is finite. The smearing affects a subset of these divergent contributions, undoing the cancellation — we show that this happens in a completely controlled and understood way. In addition, we present a novel generalization of the gradient flows, by extending the diffusion-like equations in a way that is compatible with all relevant symmetries. These generalized flows retain the attractive properties of the ‘standard’ gradient flows and, on top of that, display interesting new features.