Quantum field theories are considered fundamental provided they remain well-defined and predictive up to highest energies. Important such examples are known as asymptotic freedom and asymptotic safety where the high energy behaviour is controlled by a free or interacting fixed point under the renormalisation group, respectively. The focus of this thesis is the prospect of asymptotic safety for gauge theories and gravity. We are particularly interested in regimes where asymptotic safety arises at parametrically small coupling such as in large-N limits, where N relates to the degrees of freedom. Specifically, in the first part, we investigate exact ultraviolet (UV) fixed points of recently discovered four-dimensional gauge Yukawa theories in the Veneziano limit of SU(N) gauge theories coupled to matter. We include higher dimensional scalar self-interactions. Our main tools are perturbation theory in conjunction with non-perturbative \functional" renormalisation group (RG) techniques. It is established that classically irrelevant couplings take well-defined interacting fixed point values of their own, despite of their non-renormalisability within perturbation theory. We also establish vacuum stability, and show that higher order couplings remain parametrically irrelevant with near-Gaussian scaling exponents. Our results provide a crucial consistency check for exact asymptotic safety of weakly coupled gauge theories. Secondly, we perform a large-N study for quantum Einstein gravity. The main novelty here is that the number of space-time dimensions D takes the role of the number of degrees of freedom. We then derive and analyse renormalisation group equations within a 1/D expansion, also comparing the so-called single and bimetric approximations and the gauge-fixing dependence of results. In either of the cases we find an asymptotically safe gravitational fixed point and a finite radius of convergence in the 1/D expansion. We discuss the consistency of our results in comparison with previous findings, and in the light of the asymptotic safety conjecture for gravity in four dimensions.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:731264 |
| Date | January 2018 |
| Creators | Büyükbeşe, Tuğba |
| Publisher | University of Sussex |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://sro.sussex.ac.uk/id/eprint/72702/ |
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