The University of Southampton
University of Southampton Institutional Repository

Fundamental aspects of asymptotic safety in quantum gravity

Fundamental aspects of asymptotic safety in quantum gravity
Fundamental aspects of asymptotic safety in quantum gravity
This thesis is devoted to exploring various fundamental issues within asymptotic safety. Firstly, we study the reconstruction problem and present two ways in which to solve it within the context of scalar field theory, by utilising a duality relation between an effective average action and a Wilsonian effective action. Along the way we also prove a duality relation between two effective average actions computed with different UV cutoff profiles. Next we investigate the requirement of background independence within the derivative expansion of conformally reduced gravity. We show that modified Ward identities are compatible with the flow equations if and only if either the anomalous dimension vanishes or the cutoff profile is chosen to be power law, and furthermore show that no solutions exist if the Ward identities are incompatible. In the compatible case, a clear reason is found why Ward identities can still forbid the existence of fixed points. By expanding in vertices, we also demonstrate that the combined equations generically become either overconstrained or highly redundant at the six-point level. Finally, we consider the asymptoticbehaviour of fixed point solutions in the f(R) approximation and explain in detail how to construct them. We find that quantum fluctuations do not decouple at large R, typically leading to elaborate asymptotic solutions containing several free parameters. Depending on the value of the endomorphism parameter, we find many other asymptotic solutions and fixed point spaces of differing dimension.
University of Southampton
Slade, Zoe Helen
bdf0251b-0bc5-47e0-99c6-7231e1149ab7
Slade, Zoe Helen
bdf0251b-0bc5-47e0-99c6-7231e1149ab7
Morris, Timothy
a9927d31-7a12-4188-bc35-1c9d3a03a6a6

Slade, Zoe Helen (2017) Fundamental aspects of asymptotic safety in quantum gravity. University of Southampton, Doctoral Thesis, 157pp.

Record type: Thesis (Doctoral)

Abstract

This thesis is devoted to exploring various fundamental issues within asymptotic safety. Firstly, we study the reconstruction problem and present two ways in which to solve it within the context of scalar field theory, by utilising a duality relation between an effective average action and a Wilsonian effective action. Along the way we also prove a duality relation between two effective average actions computed with different UV cutoff profiles. Next we investigate the requirement of background independence within the derivative expansion of conformally reduced gravity. We show that modified Ward identities are compatible with the flow equations if and only if either the anomalous dimension vanishes or the cutoff profile is chosen to be power law, and furthermore show that no solutions exist if the Ward identities are incompatible. In the compatible case, a clear reason is found why Ward identities can still forbid the existence of fixed points. By expanding in vertices, we also demonstrate that the combined equations generically become either overconstrained or highly redundant at the six-point level. Finally, we consider the asymptoticbehaviour of fixed point solutions in the f(R) approximation and explain in detail how to construct them. We find that quantum fluctuations do not decouple at large R, typically leading to elaborate asymptotic solutions containing several free parameters. Depending on the value of the endomorphism parameter, we find many other asymptotic solutions and fixed point spaces of differing dimension.

Text
Final thesis - Version of Record
Available under License University of Southampton Thesis Licence.
Download (1MB)

More information

Published date: September 2017

Identifiers

Local EPrints ID: 415859
URI: http://eprints.soton.ac.uk/id/eprint/415859
PURE UUID: b3983f07-361d-4fcf-8d6c-cdf621caff18
ORCID for Timothy Morris: ORCID iD orcid.org/0000-0001-6256-9962

Catalogue record

Date deposited: 27 Nov 2017 17:30
Last modified: 14 Mar 2019 01:55

Export record

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×