Simplifying multiloop integrands and ultraviolet divergences of gauge theory and gravity amplitudes
Simplifying multiloop integrands and ultraviolet divergences of gauge theory and gravity amplitudes
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DOI：
10.1103/physrevd.85.105014
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发表时间：
2012-01
影响因子：
5
通讯作者：
Z. Bern;Z. Bern;Z. Bern;J. J. Carrasco-J.;J. J. Carrasco-J.;L. Dixon;L. Dixon;H. Johansson;H. Johansson-H
中科院分区：
文献类型：
--
作者：
Z. Bern;Z. Bern;Z. Bern;J. J. Carrasco-J.;J. J. Carrasco-J.;L. Dixon;L. Dixon;H. Johansson;H. Johansson-H
我们利用颜色和运动学之间的对偶性来简化 N = 4 超杨米尔斯理论的完整四环四点振幅的构造，包括非平面贡献。对偶性仅用两个平面图就完全确定了幅度的被积函数。明显的双规范理论振幅的存在使得相应的 N = 8 超重力被积函数的构造变得微不足道，其图形分子是 N = 4 超杨米尔斯分子的双倍副本（正方形）。该过程的成功提供了进一步的重要证据，证明对偶性和双拷贝属性在循环级别保持不变。四环四点超重力振幅的新形式使得与相应的N=4超杨米尔斯振幅具有相同的紫外线功率计数。我们确定振幅的紫外极点处于 D = 11/2 的临界尺寸，与 N = 4 超杨-米尔斯理论的尺寸相同。引人注目的是，完全相同的真空积分组合（简化后）将 N = 8 超重力的紫外线发散描述为 N = 4 超杨米尔斯理论中的 subleading-in-1/N{sub c}{sup 2} 单迹发散。
We use the duality between color and kinematics to simplify the construction of the complete four-loop four-point amplitude of N = 4 super-Yang-Mills theory, including the nonplanar contributions. The duality completely determines the amplitude's integrand in terms of just two planar graphs. The existence of a manifestly dual gauge-theory amplitude trivializes the construction of the corresponding N = 8 supergravity integrand, whose graph numerators are double copies (squares) of the N = 4 super-Yang-Mills numerators. The success of this procedure provides further nontrivial evidence that the duality and double-copy properties hold at loop level. The new form of the four-loop four-point supergravity amplitude makes manifest the same ultraviolet power counting as the corresponding N = 4 super-Yang-Mills amplitude. We determine the amplitude's ultraviolet pole in the critical dimension of D = 11/2, the same dimension as for N = 4 super-Yang-Mills theory. Strikingly, exactly the same combination of vacuum integrals (after simplification) describes the ultraviolet divergence of N = 8 supergravity as the subleading-in-1/N{sub c}{sup 2} single-trace divergence in N = 4 super-Yang-Mills theory.