Two-loop polygon Wilson loops in = 4 SYM
Two-loop polygon Wilson loops in = 4 SYM
复制标题
两环多边形威尔逊环 = 4 SYM
DOI：
10.1088/1126-6708/2009/05/115
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发表时间：
2009
影响因子：
5.4
通讯作者：
Anastasiou C
中科院分区：
文献类型：
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作者：
Anastasiou C
本文首次用有效的数值方法计算了Script N= 4超对称Yang-Mills理论中任意N -gon类光Wilson环的双环修正。计算的动机是由于在两个环上观察到的六边形威尔逊环的有限部分与平面六点MHV幅值之间的显著一致性。在n= 6时，我们确认ABDK/BDS分析必须通过添加剩余函数来纠正，该函数仅取决于运动变量的保形不变比率。我们数值计算了剩余函数form = 7,8，并验证了对偶共形不变性。此外，我们研究了威尔逊环剩余函数的简单和多重共线极限，并证明了它们具有相应的两环点振幅共线分解所需的精确形式。构成n-gon Wilson循环的不同图拓扑的数量不随n的增加而增加，并且有固定数量的“主积分”，我们已经计算过了。因此，我们基本上计算了一般多边形Wilson循环，如果与振幅的对应关系继续保持不变，则脚本N= 4理论中的所有平面N点双环MHV振幅。
We compute for the first time the two-loop corrections to arbitrary n-gon lightlike Wilson loops in Script N= 4 supersymmetric Yang-Mills theory, using efficient numerical methods. The calculation is motivated by the remarkable agreement between the finite part of planar six-point MHV amplitudes and hexagon Wilson loops which has been observed at two loops. At n= 6 we confirm that the ABDK/BDS ansatz must be corrected by adding a remainder function, which depends only on conformally invariant ratios of kinematic variables. We numerically compute remainder functions forn= 7, 8 and verify dual conformal invariance. Furthermore, we study simple and multiple collinear limits of the Wilson loop remainder functions and demonstrate that they have precisely the form required by the collinear factorisation of the corresponding two-loopn-point amplitudes. The number of distinct diagram topologies contributing to the n-gon Wilson loops does not increase with n, and there is a fixed number of``master integrals", which we have computed. Thus we have essentially computed general polygon Wilson loops, and if the correspondence with amplitudes continues to hold, all planar n-point two-loop MHV amplitudes in the Script N= 4 theory.