Lectures in Quantum Gravity

TL;DR

This collection surveys the foundations and frontiers of quantum gravity through six Nordita mini-courses. It starts with perturbative quantum gravity and the gravitational EFT, then analyzes strictly renormalizable quadratic gravity as a UV-complete candidate, and finally discusses nonperturbative UV scenarios (asymptotic safety) and string theory, complemented by quantum effects in black hole spacetimes. The text emphasizes coherent connections across approaches, using consistent conventions, propagator constructions, gauge choices, unitarity considerations, and positivity bounds to relate low-energy EFTs to potential UV completions. It highlights the roles of ghosts, field redefinitions, and various quantization schemes, while stressing falsifiability and observational implications such as tensor-to-scalar ratios in cosmology, thereby linking theoretical consistency with potential experiments.

Abstract

Formulating a quantum theory of gravity lies at the heart of fundamental theoretical physics. This collection of lecture notes encompasses a selection of topics that were covered in six mini-courses at the Nordita PhD school "Towards Quantum Gravity". The scope was to provide a coherent picture, from its foundation to forefront research, emphasizing connections between different areas. The lectures begin with perturbative quantum gravity and effective field theory. Subsequently, two ultraviolet-complete approaches are presented: asymptotically safe gravity and string theory. Finally, elements of quantum effects in black hole spacetimes are discussed.

Figures (37)

• Figure 2.1: (a) Tadpole diagram; (b) bubble diagram; (c) one-loop three-vertex diagram with external lines attached to three-vertices; (d) one-loop three-vertex diagram with one external line attached to a three-vertex and two external lines attached to a four-vertex. Wavy external lines correspond to gravitons, while the solid internal lines correspond to either graviton or Faddeev-Popov propagators.
• Figure 2.2: Set of diagrams that contribute with logarithmic divergences to the divergent part of the two-loop quantum effective action. Wavy external lines correspond to gravitons, while the solid internal lines correspond to either graviton or Faddeev-Popov propagators.
• Figure 3.1: EFT description, range of validity, properties and proposals for UV completions.
• Figure 3.2: Feynman rules for minimally coupled scalar.
• Figure 3.3: $t$-channel graviton exchange diagram contributing to \ref{['graviton-mediated amplitude']}.