Quantum fields in the non-perturbative regime - Yang-Mills theory and gravity

TL;DR

This thesis explores non-perturbative aspects of Yang-Mills theories and asymptotically safe quantum gravity using functional Renormalisation Group methods, revealing insights into confinement, phase transitions, and observational constraints.

Contribution

It provides new non-perturbative analyses of Yang-Mills confinement and phase transitions, and extends quantum gravity studies to include ghost sectors and matter couplings, linking theory to observations.

Findings

Gluon condensate formation in SU(3) Yang-Mills theory

Insights into the order of deconfinement phase transitions

Constraints on quantum gravity models from light fermions

Abstract

In this thesis we investigate two different sets of physics questions, aiming at a better understanding of the low-energy behaviour of Yang-Mills theories, and the properties connected to confinement, in a first part. In a second part, we consider asymptotically safe quantum gravity, which is a proposal for a UV completion of gravity, based on the existence of an interacting UV fixed point in the Renormalisation Group flow. Both theories are characterised by non-perturbative behaviour, the first in the IR, the second in the UV, thus we apply a functional Renormalisation Group equation which is valid beyond the perturbative regime. We investigate the ground state of SU(3) Yang-Mills theory, finding the formation of a gluon condensate, which we connect to a model for quark confinement. We further investigate the deconfinement phase transition at finite temperature for several gauge groups and shed light on the question what determines the order of the phase transition. Within quantum gravity, we examine the properties of the Faddeev-Popov ghost sector in a non-perturbative regime, thus extending truncations of Renormalisation Group flows into a new set of directions in theory space. Finally we establish a connection of quantum gravity to observations of matter, by coupling fermions to gravity. Here we use the existence of light fermions - an observationally well-established fact in our universe - to impose constraints on quantum theories of gravity.