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Covariant color-kinematics duality

Cheung, Clifford and Mangan, James (2021) Covariant color-kinematics duality. Journal of High Energy Physics, 2021 (11). Art. No. 69. ISSN 1126-6708. doi:10.1007/JHEP11(2021)069.

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We show that color-kinematics duality is a manifest property of the equations of motion governing currents and field strengths. For the nonlinear sigma model (NLSM), this insight enables an implementation of the double copy at the level of fields, as well as an explicit construction of the kinematic algebra and associated kinematic current. As a byproduct, we also derive new formulations of the special Galileon (SG) and Born-Infeld (BI) theory. For Yang-Mills (YM) theory, this same approach reveals a novel structure — covariant color-kinematics duality — whose only difference from the conventional duality is that 1/□ is replaced with covariant 1/D². Remarkably, this structure implies that YM theory is itself the covariant double copy of gauged biadjoint scalar (GBAS) theory and an F3 theory of field strengths encoding a corresponding kinematic algebra and current. Directly applying the double copy to equations of motion, we derive general relativity (GR) from the product of Einstein-YM and F3 theory. This exercise reveals a trivial variant of the classical double copy that recasts any solution of GR as a solution of YM theory in a curved background. Covariant color-kinematics duality also implies a new decomposition of tree-level amplitudes in YM theory into those of GBAS theory. Using this representation we derive a closed-form, analytic expression for all BCJ numerators in YM theory and the NLSM for any number of particles in any spacetime dimension. By virtue of the double copy, this constitutes an explicit formula for all tree-level scattering amplitudes in YM, GR, NLSM, SG, and BI.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Cheung, Clifford0000-0002-9983-9425
Mangan, James0000-0002-9713-7446
Additional Information:© 2021 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received 18 September 2021; Accepted 26 October 2021; Published 10 November 2021. We are grateful to Zvi Bern, J.J. Carrasco, Lance Dixon, Andreas Helset, Julio Parra-Martinez, Radu Roiban, Ira Rothstein, and Mikhail Solon for useful discussions and comments on the paper. C.C. and J.M. are supported by the DOE under grant no. DESC0011632 and by the Walter Burke Institute for Theoretical Physics.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Subject Keywords:Scattering Amplitudes; Duality in Gauge Field Theories; Gauge-gravity correspondence
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Issue or Number:11
Record Number:CaltechAUTHORS:20210922-182148016
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Official Citation:Cheung, C., Mangan, J. Covariant color-kinematics duality. J. High Energ. Phys. 2021, 69 (2021).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:110987
Deposited By: Joy Painter
Deposited On:22 Sep 2021 18:50
Last Modified:15 Nov 2021 21:01

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