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Coherent states, background fields, and double copy

Anton Ilderton, William Lindved

TL;DR

This work proposes a framework in which scattering amplitudes with coherent-state background fields in gauge theory double copy to amplitudes in axio-dilaton gravity on curved backgrounds, via an amplitude-level classical double copy. By representing backgrounds with coherent-state profiles, the authors extend the BCJ double copy to backgrounds, showing that vacuum double-copy relations extend to background-field amplitudes and relate the gauge background $A_ u^a(x)$ to a gravitational background comprising $h_{ ho au}(x)$, $B_{ ho au}(x)$, and $ ablaeta$-related scalars. A key result is that the gravity profiles are determined by $eta_P(k) = extstyle extstyleeta_P(k) = extstyle extstyle C_P^s \, ig( ext{gauge profile}ig)$, with an explicit mapping $eta'_P(k) = extstyle extstyleeta_P(k)$ governing the coherent-state double copy, and that the full coherent-state amplitude $\\mathscr{A}$ maps to a gravity coherent-state amplitude $\mathscr{M}$ up to a normalisation. The classical double copy emerges naturally: doubling the polarization data while keeping scalar pieces fixed yields a gravity background consistent with Kerr-Schild and self-dual structures, including plane waves and double Kerr-Schild forms, thereby linking quantum amplitude structures to classical gravity solutions. Overall, the framework offers a practical route to compute gravitational amplitudes in curved backgrounds by leveraging established vacuum double-copy relations, while enriching the landscape of classical double-copy constructions with coherent-state backgrounds and axio-dilaton content.

Abstract

We show that scattering amplitudes on any gauge theory background admitting a coherent state description double copy to amplitudes in a curved spacetime. The metric of the spacetime is built from the gauge background using a notion of classical double copy which emerges naturally at the amplitude level. In the self-dual sector this map relates backgrounds which are exact vacuum solutions in gauge theory and gravity.

Coherent states, background fields, and double copy

TL;DR

This work proposes a framework in which scattering amplitudes with coherent-state background fields in gauge theory double copy to amplitudes in axio-dilaton gravity on curved backgrounds, via an amplitude-level classical double copy. By representing backgrounds with coherent-state profiles, the authors extend the BCJ double copy to backgrounds, showing that vacuum double-copy relations extend to background-field amplitudes and relate the gauge background to a gravitational background comprising , , and -related scalars. A key result is that the gravity profiles are determined by , with an explicit mapping governing the coherent-state double copy, and that the full coherent-state amplitude maps to a gravity coherent-state amplitude up to a normalisation. The classical double copy emerges naturally: doubling the polarization data while keeping scalar pieces fixed yields a gravity background consistent with Kerr-Schild and self-dual structures, including plane waves and double Kerr-Schild forms, thereby linking quantum amplitude structures to classical gravity solutions. Overall, the framework offers a practical route to compute gravitational amplitudes in curved backgrounds by leveraging established vacuum double-copy relations, while enriching the landscape of classical double-copy constructions with coherent-state backgrounds and axio-dilaton content.

Abstract

We show that scattering amplitudes on any gauge theory background admitting a coherent state description double copy to amplitudes in a curved spacetime. The metric of the spacetime is built from the gauge background using a notion of classical double copy which emerges naturally at the amplitude level. In the self-dual sector this map relates backgrounds which are exact vacuum solutions in gauge theory and gravity.

Paper Structure

This paper contains 14 sections, 87 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Coherent states and amplitudes
  3. Perturbation theory with coherent states
  4. Perturbation theory in background fields
  5. Double copy
  6. Polarisation and colour
  7. Double copy for backgrounds
  8. Emergence of classical double copy
  9. To square or not to square
  10. Plane waves
  11. Self-dual backgrounds and Kerr-Schild
  12. Example: focus waves
  13. Double Kerr-Schild
  14. Conclusions

Figures (1)

  • Figure 1: A selection of diagrams in $2\to 2$ Compton scattering of quarks and gluons. External gluons belonging to the coherent states are marked with a cross. The rightmost diagram is not SMC and does not need to be computed, as per the final line of (\ref{['SMC-first-def']}).