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.

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字符串、扩展对象和经典双副本

我们将 Shen 最近的经典双副本公式 (arXiv:1806.07388) 基于显式颜色运动学二元性扩展到具有非零自旋的有限大小源的情况。对于自旋杨米尔斯源的情况，最普遍的一致双副本由带有自旋自由度对的引力物体组成。我们发现这些物体与背景场的耦合与经典（即重）闭合玻色弦的耦合相匹配，这表明对与颜色运动学二元性相关的源的弦理论解释。作为一种特殊情况，我们确定了一个极限，对应于无方向的弦，其中 2 型 Kalb-Ramond 轴子场与双副本的引力侧解耦。最后，我们将经典的双重复制应用于扩展对象，通过在世界线有效理论中添加有限大小的算子来描述。我们发现颜色到运动学映射的一致性要求潮汐算子的威尔逊系数服从一定的关系，这表明杨米尔斯双副本产生的扩展引力物体并不完全通用。