Spinors, Doppelgängers and the Non-Perturbative Classical Double Copy
Abstract
We develop a geometric and spinorial formulation of the non-perturbative classical double copy between the Corrigan--Fairlie--'t Hooft--Wilczek sector of complexified SU(2) Yang--Mills theory and four-dimensional conformally flat gravity. We identify the gauge potential with the positive-chiral spin connection of the conformally flat metric, establishing an exact relation between the Yang--Mills field strength and the chiral projection of the Riemann tensor. This provides a four-dimensional realisation of the doppelgänger viewpoint, in which gauge and gravitational fields arise from different interpretations of common connection data. Within this sector, the sourceless Yang--Mills equations require constant scalar curvature, explaining the shared nonlinear scalar equation and extending the gravitational correspondence from traceless matter to matter with constant energy--momentum trace. By representing adjoint colour indices as symmetric pairs of spinor indices, we derive exact relations mapping the gauge field-strength spinors to the scalar-curvature and trace-free Ricci components of the gravitational curvature. These relations retain nontrivial curvature information despite the vanishing Weyl tensor. We illustrate the construction using anti-de Sitter and de Sitter spacetimes, together with AdS3×ℝ supported by a scalar field, demonstrating the extension to matter with nonzero constant trace
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BibTeX
@misc{armstrongwilliams2026spinors,
title = {{Spinors, Doppelgängers and the Non-Perturbative Classical Double Copy}},
author = {Kymani Armstrong-Williams},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23384},
eprint = {2610.23384},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23384},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spinors, Doppelgängers and the Non-Perturbative Classical Double Copy
AU - Kymani Armstrong-Williams
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23384
UR - https://arxiv.org/abs/2610.23384
AB - We develop a geometric and spinorial formulation of the non-perturbative classical double copy between the Corrigan--Fairlie--'t Hooft--Wilczek sector of complexified SU(2) Yang--Mills theory and four-dimensional conformally flat gravity. We identify the gauge potential with the positive-chiral spin connection of the conformally flat metric, establishing an exact relation between the Yang--Mills field strength and the chiral projection of the Riemann tensor. This provides a four-dimensional realisation of the doppelgänger viewpoint, in which gauge and gravitational fields arise from different interpretations of common connection data. Within this sector, the sourceless Yang--Mills equations require constant scalar curvature, explaining the shared nonlinear scalar equation and extending the gravitational correspondence from traceless matter to matter with constant energy--momentum trace. By representing adjoint colour indices as symmetric pairs of spinor indices, we derive exact relations mapping the gauge field-strength spinors to the scalar-curvature and trace-free Ricci components of the gravitational curvature. These relations retain nontrivial curvature information despite the vanishing Weyl tensor. We illustrate the construction using anti-de Sitter and de Sitter spacetimes, together with AdS_3×ℝ supported by a scalar field, demonstrating the extension to matter with nonzero constant trace
ER -