Strings, extended objects, and the classical double copy

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 non-zero 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 color-kinematics 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.

14+4 pages, 4 figures. v3: corrected typos, same as the JHEP version

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• Scattering Amplitudes and Conservative Binary Dynamics at $\mathcal{O}(G^4)$
• A Twistorial Foundation for the Classical Double Copy
• Conservative Binary Dynamics with a Spinning Black Hole at $\mathcal{O}(G^3)$ from Scattering Amplitudes
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• Kaluza-Klein from Colour-Kinematics Duality for Massive Fields
• Classical Gravitational Self-Energy from Double Copy
• Scattering of Gravitons and Spinning Massive States from Compact Numerators
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• The Kerr-Schild Double Copy in Lifshitz Spacetime