Quantum gravity, effective fields and string theory

TL;DR

This work treats general relativity as an effective field theory to extract calculable low-energy quantum gravity effects, including leading quantum corrections to the Schwarzschild and Kerr metrics and the non-analytic contributions to the gravitational scattering potential. It extends gauge–gravity relations via Kawai–Lewellen–Tye (KLT) mappings to the EFT setting, deriving generalized tree-level correspondences between gravity and Yang–Mills operators and illustrating how higher-derivative terms coherently map between the two theories. A separate thread explores gravity in the limit of infinitely many spatial dimensions, identifying the dominant diagram classes in the large-$D$ expansion and connecting it to an effective, renormalizable framework with practical computational benefits. Collectively, the thesis demonstrates that gravity, when treated as an EFT, yields unique, testable quantum signatures at low energies and offers a coherent bridge to gauge theories and string-inspired structures, while acknowledging the role of high-energy completions like string theory. The results illuminate how quantum gravity can be probed indirectly through EFT techniques, and outline paths for future work in EFT gravity, KLT generalizations, and large-$D$ analyses.

Abstract

We look at the various aspects of treating general relativity as a quantum theory. It is briefly studied how to consistently quantize general relativity as an effective field theory. A key achievement here is the long-range low-energy leading quantum corrections to both the Schwarzschild and Kerr metrics. The leading quantum corrections to the pure gravitational potential between two sources are also calculated, both in the mixed theory of scalar QED and quantum gravity and in the pure gravitational theory. The (Kawai-Lewellen-Tye) string theory gauge/gravity relations is next dealt with. We investigate if the KLT-operator mapping extends to the case of higher derivative effective operators. The KLT-relations are generalized, taking the effective field theory viewpoint, and remarkable tree-level amplitude relations between the field theory operators are derived. Quantum gravity is finally looked at from the the perspective of taking the limit of infinitely many spatial dimensions. It is verified that only a certain class of planar graphs will in fact contribute to the $n$-point functions at $D=\infty$. This limit is somewhat an analogy to the large-N limit of gauge theories although the interpretation of such a graph limit in a gravitational framework is quite different.

Figures (52)

• Figure 1: Illustration of the gravitational attraction between two sources, with or without a kinetic energy.
• Figure 2: Illustration of light rays bending around the Sun.
• Figure 3: Feynman's double slit experiment, see ref. Feynman. An experiment to illustrate intuitively why the Universe fundamentally must be of a classical or of a quantum nature, $i.e.$, a combined description is not possible. If gravitational waves from the quantum particle in the experiment are classical, there is something wrong from a quantum mechanical perspective, because when we in principle could detect which slit the quantum particle went. This would disagree with the principles of quantum mechanics. On the other hand if the wave-detector senses gravitational waves, with a quantum nature, $i.e.$, wave amplitudes, surely gravity self must be a quantum theory for the experiment to be consistent! Thus a fundamental theory for gravity has to be a quantum theory, if we assume that all other theories of Nature are quantum theories.
• Figure 4: The only gravitational radiative diagrams which carry non-analytic contributions.
• Figure 5: The only gravitational radiative diagrams which carry non-analytic contributions.