Strings, extended objects, and the classical double copy

TL;DR

This paper extends the classical double copy framework to include finite-size, spinning sources, revealing connections to string theory and imposing constraints on extended gravitating objects.

Contribution

It generalizes the classical double copy to spinning and extended objects, linking them to string theory and identifying conditions on their properties.

Findings

Double copy for spinning sources involves pairs of spin degrees of freedom.

Couplings of spinning sources match those of a classical closed bosonic string.

Consistency conditions impose relations on tidal operator coefficients.

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.