Towards a non-perturbative classical double copy
- 1Queen Mary University of London
Abstract
We construct an exact solution-generating correspondence between restricted ansatz sectors of quartic biadjoint scalar theory, complexified SU (2) Yang-Mills theory and four-dimensional general relativity with conformally flat metrics and traceless energy-momentum. A factorised biadjoint field, a Corrigan-Fairlie-’t Hooft-Wilczek gauge potential and a conformal metric are generated by a common scalar seed. Their equations of motion reduce to the same equation of motion under the identification of couplings, which retains the nonlinear dynamics on all three legs of the correspondence. The scalar equation captures only the trace of the Einstein equations; deriving the trace-free part of the Einstein equation additionally yields a source relation between Gravity and Yang-Mills. From this, we construct a non-perturbative classical double copy for the restricted ansatz sectors between quartic biadjoint scalar theory, SU (2) Yang-Mills theory and gravity. We illustrate the dictionary of mappable solutions with rational and constant profiles representing AdS4, planar dS4 and Minkowski space, and with Jacobi-elliptic profiles generating a positive-energy recollapsing branch for negative cosmological constant and a negative-energy bouncing branch for positive cosmological constant. Using these results, we provide a new example of the Kerr-Schild double copy.
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BibTeX
@article{armstrongwilliams2026towards,
title = {{Towards a non-perturbative classical double copy}},
author = {Kymani Armstrong-Williams},
journal = {Journal of High Energy Physics},
year = {2026},
month = oct,
doi = {10.1007/jhep10(2026)269},
url = {https://link.springer.com/article/10.1007/JHEP10(2026)269},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Towards a non-perturbative classical double copy
AU - Kymani Armstrong-Williams
PY - 2026
DA - 2026/10/28
JO - Journal of High Energy Physics
DO - 10.1007/jhep10(2026)269
UR - https://link.springer.com/article/10.1007/JHEP10(2026)269
AB - We construct an exact solution-generating correspondence between restricted ansatz sectors of quartic biadjoint scalar theory, complexified SU (2) Yang-Mills theory and four-dimensional general relativity with conformally flat metrics and traceless energy-momentum. A factorised biadjoint field, a Corrigan-Fairlie-’t Hooft-Wilczek gauge potential and a conformal metric are generated by a common scalar seed. Their equations of motion reduce to the same equation of motion under the identification of couplings, which retains the nonlinear dynamics on all three legs of the correspondence. The scalar equation captures only the trace of the Einstein equations; deriving the trace-free part of the Einstein equation additionally yields a source relation between Gravity and Yang-Mills. From this, we construct a non-perturbative classical double copy for the restricted ansatz sectors between quartic biadjoint scalar theory, SU (2) Yang-Mills theory and gravity. We illustrate the dictionary of mappable solutions with rational and constant profiles representing AdS4, planar dS4 and Minkowski space, and with Jacobi-elliptic profiles generating a positive-energy recollapsing branch for negative cosmological constant and a negative-energy bouncing branch for positive cosmological constant. Using these results, we provide a new example of the Kerr-Schild double copy.
SN - 1029-8479
ER -