He Song, Schlotterer Oliver
CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics & UCAS, Chinese Academy of Sciences, Beijing 100190, China.
Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, 14476 Potsdam, Germany.
Phys Rev Lett. 2017 Apr 21;118(16):161601. doi: 10.1103/PhysRevLett.118.161601.
In this Letter, we extend the tree-level Kawai-Lewellen-Tye (KLT) and Bern-Carrasco-Johansson (BCJ) amplitude relations to loop integrands of gauge theory and gravity. By rearranging the propagators of gauge and gravity loop integrands, we propose the first manifestly gauge- and diffeomorphism-invariant formulation of their double-copy relations. The one-loop KLT formula expresses gravity integrands in terms of more basic gauge invariant building blocks for gauge-theory amplitudes, dubbed partial integrands. The latter obey a one-loop analogue of the BCJ relations, and both KLT and BCJ relations are universal to bosons and fermions in any number of spacetime dimensions and independent on the amount of supersymmetry. Also, one-loop integrands of Einstein-Yang-Mills theory are related to partial integrands of pure gauge theories.
在本信函中，我们将树图级别的河合-勒韦伦-泰（KLT）和伯恩-卡拉斯科-约翰松（BCJ）振幅关系扩展到规范理论和引力的圈积分项。通过重新排列规范和引力圈积分项的传播子，我们提出了它们双拷贝关系的首个明显规范不变和微分同胚不变的表述。单圈KLT公式用规范理论振幅的更基本规范不变构建块（称为部分积分项）来表示引力积分项。后者服从BCJ关系的单圈类似物，并且KLT和BCJ关系对于任意时空维度的玻色子和费米子都是通用的，且与超对称的数量无关。此外，爱因斯坦-杨-米尔斯理论的单圈积分项与纯规范理论的部分积分项相关。
