Fundamental Aspects of Asymptotic Safety in Quantum Gravity
Zo\"e H. Slade
TL;DR
This thesis investigates fundamental issues in asymptotic safety for quantum gravity, including duality relations, background independence, Ward identities, and the asymptotic behavior of fixed points, providing new insights into the structure of quantum gravity theories.
Contribution
It introduces novel duality relations in effective actions, analyzes background independence constraints, and explores the asymptotic structure of fixed points in quantum gravity within the asymptotic safety framework.
Findings
Proved duality relations between effective average actions with different UV cutoffs.
Identified conditions under which Ward identities are compatible with flow equations in conformally reduced gravity.
Constructed and analyzed asymptotic solutions for fixed points in the $f(R)$ approximation.
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…
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Taxonomy
TopicsCosmology and Gravitation Theories · Stochastic processes and financial applications · Quantum Chromodynamics and Particle Interactions
\supervisor
Tim R. Morris \degreeDoctor of Philosophy \universityUniversity of Southampton \facultyFaculty of Science and Engineering \academicunitPhysics and Astronomy
Fundamental Aspects of Asymptotic Safety in Quantum Gravity
Zoë Helen Slade
(January 2017)
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 over-constrained or highly redundant at the six-point level. Finally, we consider the asymptotic behaviour of fixed point solutions in the approximation and explain in detail how to construct them. We find that quantum fluctuations do not decouple at large , 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.
\authorshipdeclaration
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Tim R. Morris, Zoë H. Slade, Solutions to the reconstruction problem in asymptotic safety. Journal of High Energy Physics 11 (2015) 904. arXiv:1507.08657 [hep-th][Morris:2015oca].
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Peter Labus, Tim R. Morris, Zoë H. Slade, Background independence in a background dependent renormalization group. Phys. Rev. D 94 (2016) 024007. arXiv:1603.04772 [hep-th] [Labus:2016lkh].
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Sergio Gonzalez-Martin, Tim R. Morris, Zoë H. Slade Asymptotic solutions in asymptotic safety. Phys. Rev. D 95 (2017) 106010. arXiv:1704.08873 [hep-th] [Gonzalez-Martin:2017gza].
Acknowledgements.
First of all, I would like to thank my supervisor Tim Morris for all his help and support over the past four years, without which none of this would have been possible. I would like to acknowledge the Women’s Physics Network, and the support it receives from the department, as well as all the opportunities I have had to take part in outreach and public engagement whilst in Southampton. All of this has undoubtedly enriched my PhD experience. Thank you to all my physics friends, past and present, who have provided stimulating conversation, endless entertainment and companionship throughout the years. Thank you also to the other friends I have made over the course of my studies here for all your support and for truly enhancing my time in Southampton. A special thank you goes to Peter Jones for always being there for me and filling these past 4 years with so much fun and laughter. I am really grateful I was able to share this adventure with you. Last, but by no means least, I would like to thank my family for their endless love, support and encouragement, without which I would not be where I am today. Thank you for all the opportunities you have given me.