Abstract
We report on progress in understanding how to construct color-dual multi-loop amplitudes. First we identify a cubic theory, semi-abelian Yang-Mills, that unifies many of the color-dual theories studied in the literature, and provides a prescriptive approach for constructing D-dimensional color-dual numerators through one-loop directly from Feynman rules. By a simple weight counting argument, this approach does not further generalize to two-loops. As a first step in understanding the two-loop challenge, we use a D-dimensional color-dual bootstrap to successfully construct globally color-dual local two-loop four-point nonlinear sigma model (NLSM) numerators. The double-copy of these NLSM numerators with themselves, pure Yang-Mills, and \(\mathcal{N}\) = 4 super-Yang-Mills correctly reproduce the known unitarity constructed integrands of special Galileons, Born-Infeld theory, and Dirac-Born-Infeld-Volkov-Akulov theory, respectively. Applying our bootstrap to two-loop four-point pure Yang-Mills, we exhaustively search the space of local numerators and find that it fails to satisfy global color-kinematics duality, completing a search previously initiated in the literature. We pinpoint the failure to the bowtie unitarity cut, and discuss a path forward towards non-local construction of color-dual integrands at generic loop order.
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Acknowledgments
The authors would like to thank John Joseph Carrasco, Sasank Chava, Clifford Cheung, Kezhu Guo, Nia Robles, Aslan Seifi, Fei Teng, and Suna Zekioğlu for insightful conversations, feedback on earlier drafts, and encouragement throughout the completion of this work. This work was supported by the DOE under contract DE-SC0015910 and by the Alfred P. Sloan Foundation. Additionally we would like to acknowledge the Northwestern University Amplitudes and Insight group, the Department of Physics and Astronomy, and Weinberg College for their generous support. Feynman diagrams were typeset using TikZ-Feynman [80].
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Edison, A., Mangan, J. & Pavao, N.H. Revealing the landscape of globally color-dual multi-loop integrands. J. High Energ. Phys. 2024, 163 (2024). https://doi.org/10.1007/JHEP03(2024)163
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DOI: https://doi.org/10.1007/JHEP03(2024)163