On the kinematic algebra for BCJ numerators beyond the MHV sector
On the kinematic algebra for BCJ numerators beyond the MHV sector
复制标题
DOI：
10.1007/jhep11(2019)055
复制
发表时间：
2019-11-11
影响因子：
5.4
通讯作者：
Wang, Tianheng
中科院分区：
文献类型：
--
作者：
Chen, Gang;Johansson, Henrik;Wang, Tianheng
杨-米尔斯理论散射振幅中的颜色和运动学之间的对偶性强烈地暗示了控制规范理论的隐藏运动学李代数的存在。虽然相关的BCJ分子是已知的封闭形式，以任何多重性在树的水平，运动代数只进行了部分探索，最简单的四维振幅：MHV部门。在本文中，我们介绍了一个框架，使我们能够描述超越MHV部门的代数。这使得我们既可以约束运动学代数的一些模糊性，又可以更好地控制与BCJ分子相关的广义规范自由度。具体而言，在本文中，我们的工作在尺寸不可知的符号，并确定运动代数有效的某些？（（i . j）（2））项，在四维中计算涉及两个标量的次MHV扇区。在这个部门的运动代数是简单的，因为我们引入张量电流，推广标准杨米尔斯矢量电流。这些张量流控制广义规范自由度，使我们能够从同一运动学代数生成多个不同版本的BCJ分子。该框架应推广到杨-米尔斯理论的其他部门。
The duality between color and kinematics present in scattering amplitudes of Yang-Mills theory strongly suggests the existence of a hidden kinematic Lie algebra that controls the gauge theory. While associated BCJ numerators are known on closed forms to any multiplicity at tree level, the kinematic algebra has only been partially explored for the simplest of four-dimensional amplitudes: up to the MHV sector. In this paper we introduce a framework that allows us to characterize the algebra beyond the MHV sector. This allows us to both constrain some of the ambiguities of the kinematic algebra, and better control the generalized gauge freedom that is associated with the BCJ numerators. Specifically, in this paper, we work in dimension-agnostic notation and determine the kinematic algebra valid up to certain ? ((epsilon i .epsilon j )(2)) terms that in four dimensions compute the next-to-MHV sector involving two scalars. The kinematic algebra in this sector is simple, given that we introduce tensor currents that generalize standard Yang-Mills vector currents. These tensor currents control the generalized gauge freedom, allowing us to generate multiple different versions of BCJ numerators from the same kinematic algebra. The framework should generalize to other sectors in Yang-Mills theory.