Bern Zvi, Carrasco John Joseph, Chen Wei-Ming, Johansson Henrik, Roiban Radu
Mani L. Bhaumik Institute for Theoretical Physics UCLA Department of Physics and Astronomy Los Angeles, California 90095, USA.
Institut de Physique Theorique, CEA-Saclay F-91191 Gif-sur-Yvette cedex, France.
Phys Rev Lett. 2017 May 5;118(18):181602. doi: 10.1103/PhysRevLett.118.181602.
Whenever the integrand of a gauge-theory loop amplitude can be arranged into a form where the Bern-Carrasco-Johansson duality between color and kinematics is manifest, a corresponding gravity integrand can be obtained simply via the double-copy procedure. However, finding such gauge-theory representations can be challenging, especially at high loop orders. Here, we show that we can, instead, start from generic gauge-theory integrands, where the duality is not manifest, and apply a modified double-copy procedure to obtain gravity integrands that include contact terms generated by violations of dual Jacobi identities. We illustrate this with three-, four- and five-loop examples in N=8 supergravity.
只要规范理论圈振幅的被积函数能够被整理成一种形式，使得色与运动学之间的伯恩 - 卡拉斯科 - 约翰松对偶性得以显现，那么通过双拷贝程序就能简单地得到相应的引力被积函数。然而，找到这样的规范理论表示可能具有挑战性，尤其是在高圈阶的情况下。在这里，我们表明，相反地，我们可以从一般的规范理论被积函数出发，在这些被积函数中对偶性并不明显，然后应用一种修正的双拷贝程序来获得引力被积函数，其中包括因对偶雅可比恒等式不成立而产生的接触项。我们在(N = 8)超引力中的三圈、四圈和五圈例子中对此进行了说明。
