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The Radiative Double Copy for Einstein-Yang-Mills Theory

David Chester

TL;DR

The paper establishes a leading-order radiative double copy between Yang-Mills–biadjoint-scalar theory and Einstein–Yang–Mills theory within a weak-field expansion, identifying the trace-reversed metric $\bar{h}^{\mu\nu}$ as the double copy of the gauge field $A^{\mu a}$. It develops a perturbative framework for classical radiation, computes the YM–biadjoint-scalar radiative currents and fields, and then derives the corresponding gravitational radiation in EYM theory. By applying explicit replacement rules, it demonstrates that the gravitational radiation source $\hat{T}^{\mu\nu}$ is reproduced from gauge theory data at leading order, confirming the radiative double-copy relation and its gauge-invariant organization via pseudotensors and three-point vertices. The work also shows how Einstein–Maxwell theory emerges as a special case and outlines prospects for extending the double copy to higher orders, potentially aiding complex gravitational-radiation calculations relevant to observations such as LIGO.

Abstract

Recently, a double-copy formalism was used to calculate gravitational radiation from classical Yang-Mills radiation solutions. This work shows that Yang-Mills theory coupled to a biadjoint scalar field admits a radiative double copy that agrees with solutions in Einstein-Yang-Mills theory at the lowest finite order. Within this context, the trace-reversed metric $\bar{h}^{μν}$ is a natural double copy of the gauge boson $A^{μa}$. This work provides additional evidence that solutions in gauge and gravity theories are related, even though their respective Lagrangians and nonlinear equations of motion appear to be different.

The Radiative Double Copy for Einstein-Yang-Mills Theory

TL;DR

The paper establishes a leading-order radiative double copy between Yang-Mills–biadjoint-scalar theory and Einstein–Yang–Mills theory within a weak-field expansion, identifying the trace-reversed metric as the double copy of the gauge field . It develops a perturbative framework for classical radiation, computes the YM–biadjoint-scalar radiative currents and fields, and then derives the corresponding gravitational radiation in EYM theory. By applying explicit replacement rules, it demonstrates that the gravitational radiation source is reproduced from gauge theory data at leading order, confirming the radiative double-copy relation and its gauge-invariant organization via pseudotensors and three-point vertices. The work also shows how Einstein–Maxwell theory emerges as a special case and outlines prospects for extending the double copy to higher orders, potentially aiding complex gravitational-radiation calculations relevant to observations such as LIGO.

Abstract

Recently, a double-copy formalism was used to calculate gravitational radiation from classical Yang-Mills radiation solutions. This work shows that Yang-Mills theory coupled to a biadjoint scalar field admits a radiative double copy that agrees with solutions in Einstein-Yang-Mills theory at the lowest finite order. Within this context, the trace-reversed metric is a natural double copy of the gauge boson . This work provides additional evidence that solutions in gauge and gravity theories are related, even though their respective Lagrangians and nonlinear equations of motion appear to be different.

Paper Structure

This paper contains 14 sections, 93 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Radiation in Yang-Mills-Biadjoint-Scalar Theory
  3. Equations of Motion and Initial Conditions
  4. Solutions of the Radiation Fields
  5. Gravitational Radiation in Einstein-Yang-Mills Theory
  6. Equations of Motion and Initial Conditions
  7. Solutions of the Radiation Fields
  8. The Radiative Double Copy
  9. Einstein-Maxwell Theory
  10. Conclusions
  11. Derivation of Gravitational Radiation from Pseudotensor
  12. Some Radiative Feynman Rules
  13. Yang-Mills and Biadjoint-Scalar Theory
  14. General Relativity and Einstein-Yang-Mills Theory

Figures (2)

  • Figure 1: These diagrams represent all of the contributions to $\hat{J}^{\mu a}$ in Yang-Mills-biadjoint-scalar theory. Straight lines represent matter fields, curly lines represent Yang-Mills fields, and doubly-dashed lines represent biadjoint scalar fields.
  • Figure 2: These diagrams represent all of the contributions to $\hat{T}^{\mu\nu}$ in Einstein-Yang-Mills theory. The wavy lines represent gravitational fields, the dashed lines represent dilaton fields and the curly lines represent Yang-Mills fields.