Effective field theories of gravity: a top-down approach
File(s)
Author(s)
Harrold, Alexander
Type
Thesis
Abstract
From water boiling to the behaviour of magnets, the world around us is often described using the language
of Effective Field Theory. This powerful framework is often employed to model a system in terms of its low
energy degrees of freedom without much thought being given to the higher energy origins of the model. In
this thesis we shall attempt to turn this idea on its head by constructing effective theories by beginning
from the high energy theory and then arriving at the low energy description. Our main aim shall be to
address this issue in the context of deriving the EFT of perturbations around a background solution of
Type IIA Supergravity given by Crampton, Pope and Stelle that involves the non-compact hyperbolic space
H 2,2 . Studying the subject of EFTs in the context of Type IIA Supergravity presents it’s own challenges as
this theory exists in ten spacetime dimensions, whilst our observed universe is four dimensional. We shall
present how to address this issue of dimensional mismatch using Kaluza-Klein methods and discuss aspects
of the resulting lower dimensional field with an eye towards achieving lower dimensional diffeomorphism
invariance. This treatment shall lead us to the conclusion that a previously undiscovered Stueckelberg field
must be accounted for and dealt with if one is to appropriately understand the lower dimensional theory. We also exhibit a generalisation of the solutions of Crampton, Pope and Stelle to include time dependence.
Such solutions may have applications to cosmological models.
of Effective Field Theory. This powerful framework is often employed to model a system in terms of its low
energy degrees of freedom without much thought being given to the higher energy origins of the model. In
this thesis we shall attempt to turn this idea on its head by constructing effective theories by beginning
from the high energy theory and then arriving at the low energy description. Our main aim shall be to
address this issue in the context of deriving the EFT of perturbations around a background solution of
Type IIA Supergravity given by Crampton, Pope and Stelle that involves the non-compact hyperbolic space
H 2,2 . Studying the subject of EFTs in the context of Type IIA Supergravity presents it’s own challenges as
this theory exists in ten spacetime dimensions, whilst our observed universe is four dimensional. We shall
present how to address this issue of dimensional mismatch using Kaluza-Klein methods and discuss aspects
of the resulting lower dimensional field with an eye towards achieving lower dimensional diffeomorphism
invariance. This treatment shall lead us to the conclusion that a previously undiscovered Stueckelberg field
must be accounted for and dealt with if one is to appropriately understand the lower dimensional theory. We also exhibit a generalisation of the solutions of Crampton, Pope and Stelle to include time dependence.
Such solutions may have applications to cosmological models.
Version
Open Access
Date Issued
2019-09
Date Awarded
2020-04
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Stelle, Kellogg
Publisher Department
Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)