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Factorization Properties of Soft Graviton Amplitudes

Chris D. White

TL;DR

Problem: IR structure of perturbative gravity and whether soft gravitons factorize similarly to gauge theories. Approach: path-integral resummation that yields external-line Wilson line operators and a factorized amplitude A = H S, with S a vacuum expectation value of Wilson lines. Results: eikonal contributions exponentiate; NE corrections from external emissions exponentiate while internal emissions are subleading; mass effects introduce additional Wilson line terms. Significance: strengthens the gravity-gauge theory correspondence, clarifies the role of massive external particles, and provides a framework for studying gravitational radiation beyond the eikonal approximation.

Abstract

We apply recently developed path integral resummation methods to perturbative quantum gravity. In particular, we provide supporting evidence that eikonal graviton amplitudes factorize into hard and soft parts, and confirm a recent hypothesis that soft gravitons are modelled by vacuum expectation values of products of certain Wilson line operators, which differ for massless and massive particles. We also investigate terms which break this factorization, and find that they are subleading with respect to the eikonal amplitude. The results may help in understanding the connections between gravity and gauge theories in more detail, as well as in studying gravitational radiation beyond the eikonal approximation.

Factorization Properties of Soft Graviton Amplitudes

TL;DR

Problem: IR structure of perturbative gravity and whether soft gravitons factorize similarly to gauge theories. Approach: path-integral resummation that yields external-line Wilson line operators and a factorized amplitude A = H S, with S a vacuum expectation value of Wilson lines. Results: eikonal contributions exponentiate; NE corrections from external emissions exponentiate while internal emissions are subleading; mass effects introduce additional Wilson line terms. Significance: strengthens the gravity-gauge theory correspondence, clarifies the role of massive external particles, and provides a framework for studying gravitational radiation beyond the eikonal approximation.

Abstract

We apply recently developed path integral resummation methods to perturbative quantum gravity. In particular, we provide supporting evidence that eikonal graviton amplitudes factorize into hard and soft parts, and confirm a recent hypothesis that soft gravitons are modelled by vacuum expectation values of products of certain Wilson line operators, which differ for massless and massive particles. We also investigate terms which break this factorization, and find that they are subleading with respect to the eikonal amplitude. The results may help in understanding the connections between gravity and gauge theories in more detail, as well as in studying gravitational radiation beyond the eikonal approximation.

Paper Structure

This paper contains 7 sections, 113 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Path integral approach to soft graviton amplitudes
  3. Factorization breaking terms
  4. Discussion
  5. NE Feynman rules from the path integral approach
  6. Diagrammatic check of the NE Feynman rules
  7. Diagrammatic derivation of eq. (\ref{['gravlow']}) for internal emissions

Figures (5)

  • Figure 1: Examples of (a) a generic hard interaction with outgoing particles, which may emit soft gauge bosons; (b) an external emission contribution; (c) an internal emission contribution.
  • Figure 2: Example external emission graphs which exponentiate at next-to-eikonal order, where $\bullet$ represents a next-to-eikonal vertex, the doubled gluon line a graviton, and all other vertices are assumed to be eikonal.
  • Figure 3: Graph used to check the one graviton emission vertex.
  • Figure 4: Graphs used to check the two graviton emission vertex.
  • Figure 5: (a) Example vertex function involving two outgoing particles; (b) Series of diagrams involving all possible placements of an extra graviton.