UV Completeness: From Quantum Field Theory to Quantum Gravity

Abstract

One of the main goals of theoretical physics is to describe physics at all energy scales. The usual renormalization scheme of quantum field theory provides a way to investigate the details of physical systems at different energy scales, potentially up to some energy cut-off. When a theory is predictive at arbitrarily high energies and hence the cut-off can be removed, we say the theory is UV complete. The importance of UV completeness lies in its ability to explain physical phenomena at arbitrarily small distances or high energies. However, when standard techniques from quantum field theory fail to provide such a description, new degrees of freedom are expected to become important. In this thesis, we investigate two types of UV completions; one associated with conformal field theories and the other with quantum gravity. For the former, we study the fixed points of the renormalization group where one needs to integrate-in light solitonic particles/strings in the context of supersymmetric conformal field theories. For the latter, we review the challenges of UV completing quantum gravity and the severe constraints that such a completion is expected to provide for the low-energy physics. The study of such constraints constitutes the idea behind the Swampland program, which aims to identify theories that are inconsistent when coupled to gravity. A guiding tool for further understanding and constructing both classes of theories is string theory, which provides a framework to analyze strongly coupled systems. In particular, it can be used to provide a classification framework for five dimensional superconformal field theories. However, string theory, being a theory of quantum gravity, can also be used to analyze the possible landscape of supergravity theories. We reconstruct some of the results suggested by string theory from bottom up and in particular focus on questions related to the finiteness of quantum gravity. Our results are suggestive of a possible string universality for supersymmetric gravitational theories.