Consistency of gravitational effective field theories
File(s)
Author(s)
Jaitly, Sumer
Type
Thesis
Abstract
Quantum field theories are most pragmatically viewed as effective field theories, accurately
describing physics within a finite range of energy or length scales. Effective field theories
describe the dynamics of low-energy (IR) degrees of freedom whilst implicitly encoding the influence of their interaction with high-energy (UV) degrees of freedom. The low-energy physics
is described by a Wilsonian effective action which can include any operator built out of these
IR degrees of freedom, with the details of the UV physics captured by their coupling constants.
From a low-energy observer’s perspective, without further input, the values of these coupling
constants could take any value, however it is known that if the UV physics satisfies consistency conditions such as unitarity, causality, locality and Lorentz invariance, then the values
are strongly restricted by ‘positivity bounds’. The usual derivation of these bounds fails for
theories including gravity due to the universal nature of massless graviton exchange. We explore two methods for circumventing these issues: the first involves compactifying space-time
to 2 + 1 dimensions, where gravity is non-dynamical, and the second involves assuming a Regge
behavior of the scattering amplitude at high energy. In the first, we find that UV consistency
conditions applied to minimally coupled quantum electrodynamics lower the cutoff of the EFT
dramatically, however we consider that this conclusion may be hindered by issues related to
gravity in 2 + 1 dimensions. On the other hand, the second method implies a fascinating connection between IR and UV physics which could imply that UV physics is controlled by the
lightest mass scales in the IR.
describing physics within a finite range of energy or length scales. Effective field theories
describe the dynamics of low-energy (IR) degrees of freedom whilst implicitly encoding the influence of their interaction with high-energy (UV) degrees of freedom. The low-energy physics
is described by a Wilsonian effective action which can include any operator built out of these
IR degrees of freedom, with the details of the UV physics captured by their coupling constants.
From a low-energy observer’s perspective, without further input, the values of these coupling
constants could take any value, however it is known that if the UV physics satisfies consistency conditions such as unitarity, causality, locality and Lorentz invariance, then the values
are strongly restricted by ‘positivity bounds’. The usual derivation of these bounds fails for
theories including gravity due to the universal nature of massless graviton exchange. We explore two methods for circumventing these issues: the first involves compactifying space-time
to 2 + 1 dimensions, where gravity is non-dynamical, and the second involves assuming a Regge
behavior of the scattering amplitude at high energy. In the first, we find that UV consistency
conditions applied to minimally coupled quantum electrodynamics lower the cutoff of the EFT
dramatically, however we consider that this conclusion may be hindered by issues related to
gravity in 2 + 1 dimensions. On the other hand, the second method implies a fascinating connection between IR and UV physics which could imply that UV physics is controlled by the
lightest mass scales in the IR.
Version
Open Access
Date Issued
2023-11
Date Awarded
2024-03
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
de Rham, Claudia
Publisher Department
Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)