Strings, extended objects, and the classical double copy
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Received: December 17, 2019 Accepted: January 30, 2020 Published: February 14, 2020
Walter D. Goldberger and Jingping Li Department of Physics, Yale University, New Haven, CT 06511, U.S.A.
E-mail: [email protected], [email protected] Abstract: We extend Shen’s recent formulation (arXiv:1806.07388) of the classical double copy, based on explicit color-kinematic duality, to the case of finite-size sources with nonzero spin. For the case of spinning Yang-Mills sources, the most general consistent double copy consists of gravitating objects which carry pairs of spin degrees of freedom. We find that the couplings of such objects to background fields match those of a classical (i.e. heavy) closed bosonic string, suggesting a string theory interpretation of sources related by colorkinematics duality. As a special case, we identify a limit, corresponding to unoriented strings, in which the 2-form Kalb-Ramond axion field decouples from the gravitational side of the double copy. Finally, we apply the classical double copy to extended objects, described by the addition of finite-size operators to the worldline effective theory. We find that consistency of the color-to-kinematics map requires that the Wilson coefficients of tidal operators obey certain relations, indicating that the extended gravitating objects generated by the double copy of Yang-Mills are not completely generic. Keywords: Classical Theories of Gravity, Effective Field Theories, Scattering Amplitudes ArXiv ePrint: 1912.01650
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP02(2020)092
JHEP02(2020)092
Strings, extended objects, and the classical double copy
Contents 1 Introduction
1
2 The classical double copy 2.1 Beyond leading order and color-kinematic duality
3 7 9 9 10
4 Dynamical polarizability and its double copy
13
5 Discussions and conclusions
18
A Radiation from higher dimensional operators A.1 Spin-dependent terms
19 21
1
Introduction
About a decade ago, Bern, Carrasco, and Johansson (BCJ) conjectured [1, 2] the existence of color-kinematics, or BCJ, duality of scattering amplitudes in perturbative Yang-Mills theories. Their work initiated the double copy program that exploits this duality to construct perturbative amplitudes in gravity theories, generalizing the earlier KLT [3] relations between open and closed string scattering amplitudes. While the BCJ double copy has been rigorously proven for all tree-level amplitudes (see for instance [4, 5]), the color-kinematic duality remains conjectural for loop amplitudes [6]. Nevertheless, many explicit checks of the conjecture at the loop level have been performed, leading to the recent study of five-loop amplitudes in refs. [7, 8]. For a comprehensive review of the current state of the field, see [9]. In particular, the BCJ double copy leverages the relative simplicity of gauge theory scattering amplitudes to improve the efficiency of obtaining results in perturbative quantum gravity that would be otherwise intractable. Naturall
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