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Relationship Between Gravity and Gauge Scattering in the High Energy Limit

Ryo Saotome, Ratindranath Akhoury

TL;DR

The paper investigates high-energy graviton-graviton and gluon-gluon scattering in the leading eikonal limit and demonstrates a gravity–gauge double copy at all loops, provided one restricts to the subset of gauge-theory diagrams with identical uncrossed ladder color structures, which ensures cancellation of collinear divergences. It derives explicit gravity and QCD amplitudes, shows their exponentiation in impact-parameter space, and establishes a BCJ-like replacement between color factors and kinematic numerators to relate the two theories. Beyond amplitudes, the work connects these results to classical shockwaves, deriving Aichelburg–Sexl-type gravitational waves and corresponding gauge shockwaves from the same eikonal framework, and revealing a consistent double-copy relation at the level of classical solutions. The findings suggest a robust, gauge-choice–dependent bridge between gravity and gauge theories in the high-energy, soft-exchange regime without invoking extra fields like the dilaton.

Abstract

Investigations of high-energy graviton-graviton and gluon-gluon scattering are performed in the leading eikonal approximation for the kinematic regime of large center of mass energy and low momentum transfer. We find a double copy relation between the amplitudes of the two theories to all loop orders when, on the gauge theory side, we retain only the set of diagrams at each loop order for which the collinear divergences cancel amongst themselves. For this to happen the color structure of all diagrams in the set must be identical. Using standard field theoretic methods, it is shown that this relation is reflected in a similar double copy relationship between the classical shockwaves of the two theories as well.

Relationship Between Gravity and Gauge Scattering in the High Energy Limit

TL;DR

The paper investigates high-energy graviton-graviton and gluon-gluon scattering in the leading eikonal limit and demonstrates a gravity–gauge double copy at all loops, provided one restricts to the subset of gauge-theory diagrams with identical uncrossed ladder color structures, which ensures cancellation of collinear divergences. It derives explicit gravity and QCD amplitudes, shows their exponentiation in impact-parameter space, and establishes a BCJ-like replacement between color factors and kinematic numerators to relate the two theories. Beyond amplitudes, the work connects these results to classical shockwaves, deriving Aichelburg–Sexl-type gravitational waves and corresponding gauge shockwaves from the same eikonal framework, and revealing a consistent double-copy relation at the level of classical solutions. The findings suggest a robust, gauge-choice–dependent bridge between gravity and gauge theories in the high-energy, soft-exchange regime without invoking extra fields like the dilaton.

Abstract

Investigations of high-energy graviton-graviton and gluon-gluon scattering are performed in the leading eikonal approximation for the kinematic regime of large center of mass energy and low momentum transfer. We find a double copy relation between the amplitudes of the two theories to all loop orders when, on the gauge theory side, we retain only the set of diagrams at each loop order for which the collinear divergences cancel amongst themselves. For this to happen the color structure of all diagrams in the set must be identical. Using standard field theoretic methods, it is shown that this relation is reflected in a similar double copy relationship between the classical shockwaves of the two theories as well.

Paper Structure

This paper contains 18 sections, 63 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Eikonal Scattering
  3. Gravity
  4. Tree Level
  5. One-Loop
  6. $n-1$ Loop
  7. Exponentiation
  8. QCD
  9. Tree Level
  10. One-Loop
  11. $n-1$ Loop
  12. Double Copy Relation
  13. Connection to Shockwaves
  14. Aichelberg-Sexl Metric
  15. Gauge Shockwave
  16. ...and 3 more sections

Figures (8)

  • Figure 1: A scattering process with a single graviton/gluon exchanged.
  • Figure 2: The box diagram.
  • Figure 3: The crossed box diagram.
  • Figure 4: The set of two-loop ladder diagrams relevant for the double copy relation in the eikonal approximation. For the same color factors the collinear divergences between these cancel.
  • Figure 5: The seagull diagram.
  • ...and 3 more figures