Quantum gravity and the renormalisation group: theoretical advances and applications

Nikolakopoulos, Konstantinos (2013) Quantum gravity and the renormalisation group: theoretical advances and applications. Doctoral thesis (PhD), University of Sussex.

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It is well known that quantisation of gravity within the conventional framework of quantum
field theory faces challenges. An intriguing novel prospect was put forward by S. Weinberg
in 1979 who suggested that the metric degrees of freedom of gravity could be quantised nonpertubatively provided that the theory becomes asymptotically safe (AS) at high energies. In this thesis we put forward a systematic search strategy to test the AS conjecture in four dimensional quantum gravity. Using modern renormalisation group (RG) methods and heat kernel techniques we derive the RG equations for gravitational actions that are formed from powers of the Ricci scalar and powers of the Ricci tensor. The non-linear fixed point equations are solved iteratively and exactly. We develop a sophisticated algorithm to express the fixed point iteratively, and to high order, in terms of its lower order couplings. We also evaluate universal scaling exponents and find that the relevancy of invariants at an asymptotically safe fixed point is governed by their classical mass dimension, providing structural support for the asymptotic safety conjecture. We also apply our findings to the physics of higher dimensional black holes. Most notably, we find that the seminal ultra-spinning Myers-Perry black holes cease to exist as soon as asymptotically safe RG corrections are taken into account. Further results and implications of our findings are discussed.

Item Type: Thesis (Doctoral)
Schools and Departments: School of Mathematical and Physical Sciences > Physics and Astronomy
Subjects: Q Science > QC Physics > QC0170 Atomic physics. Constitution and properties of matter Including molecular physics, relativity, quantum theory, and solid state physics
Depositing User: Library Cataloguing
Date Deposited: 14 Feb 2014 12:48
Last Modified: 17 Sep 2015 15:28
URI: http://sro.sussex.ac.uk/id/eprint/47448

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