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The effective field theory treatment of quantum gravity

John F. Donoghue

TL;DR

This work presents general relativity as an effective field theory, showing how low-energy quantum gravity can be described by a local, higher-derivative Lagrangian with coefficients encoding unknown UV physics.Using the linear sigma model as an explicit EFT example, it demonstrates matching of full and effective theories, loop renormalization, and power counting that organizes predictions in a controlled energy expansion.For gravity, it derives the structure of the gravitational action, one-loop finiteness in pure gravity, and concrete low-energy predictions such as the graviton scattering amplitude and the leading quantum correction to the Newton potential, independent of UV details.The article also clarifies the nonuniversality of gravitational running with energy, discusses limits of EFT near the Planck scale, and situates gravitational EFT within broader contexts such as chiral perturbation theory and potential UV completions like string theory.Overall, EFT reframes quantum gravity as a reliable, scale-separated framework at ordinary energies, while underscoring the need for a complete high-energy theory to resolve Planck-scale physics.

Abstract

This is a pedagogical introduction to the treatment of quantum general relativity as an effective field theory. It starts with an overview of the methods of effective field theory and includes an explicit example. Quantum general relativity matches this framework and I discuss gravitational examples as well as the limits of the effective field theory. I also discuss the insights from effective field theory on the gravitational effects on running couplings in the perturbative regime.

The effective field theory treatment of quantum gravity

TL;DR

This work presents general relativity as an effective field theory, showing how low-energy quantum gravity can be described by a local, higher-derivative Lagrangian with coefficients encoding unknown UV physics.Using the linear sigma model as an explicit EFT example, it demonstrates matching of full and effective theories, loop renormalization, and power counting that organizes predictions in a controlled energy expansion.For gravity, it derives the structure of the gravitational action, one-loop finiteness in pure gravity, and concrete low-energy predictions such as the graviton scattering amplitude and the leading quantum correction to the Newton potential, independent of UV details.The article also clarifies the nonuniversality of gravitational running with energy, discusses limits of EFT near the Planck scale, and situates gravitational EFT within broader contexts such as chiral perturbation theory and potential UV completions like string theory.Overall, EFT reframes quantum gravity as a reliable, scale-separated framework at ordinary energies, while underscoring the need for a complete high-energy theory to resolve Planck-scale physics.

Abstract

This is a pedagogical introduction to the treatment of quantum general relativity as an effective field theory. It starts with an overview of the methods of effective field theory and includes an explicit example. Quantum general relativity matches this framework and I discuss gravitational examples as well as the limits of the effective field theory. I also discuss the insights from effective field theory on the gravitational effects on running couplings in the perturbative regime.

Paper Structure

This paper contains 15 sections, 35 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Effective field theory in general
  3. Constructing an explicit effective field theory - the sigma model
  4. Example of the equivalence
  5. Construction of the effective theory
  6. Loops and renormalization
  7. Power counting and the energy expansion
  8. Effective field theory in action
  9. Summary of general procedures
  10. Gravity as an effective field theory
  11. Quantization and renormalization
  12. Predictions of the effective field theory
  13. Issues in the gravitational effective field theory
  14. Gravitational corrections and running coupling constants
  15. Summary

Figures (3)

  • Figure 1: Diagrams for $\pi -\pi$ scattering
  • Figure 2: The tree-level effect of the exchange of a heavy scalar, $\sigma$. The $\times$ represents a vertex involving pions, as described in the text.
  • Figure 3: a) A finite box diagram which occurs in the full theory, b) A bubble diagram which occurs in the effective theory in the situation when the propagator of the heavy $\sigma$ has been shrunken to a point.