论文标题
五角大楼威尔逊循环与拉格朗日插入$ {\ mathcal n} = 4 $ super yang-mills理论
Pentagon Wilson loop with Lagrangian insertion at two loops in ${\mathcal N}=4$ super Yang-Mills theory
论文作者
论文摘要
我们用拉格朗日插入(由Wilson Loop未经插入的Wilson Loop标准化)计算了无效的五角大楼Wilson环的两循环结果,最大程度地超对称的Yang-Mills理论。这种有限的可观察到的可观察到与扩增子密切相关的,它让人联想到平面两环五粒子散射幅度的有限部分。我们验证,直到这个循环顺序,领先的奇异性是由出现在全额外的Yang-Mills振幅中的同构形式不变的表达式给出的。伴随的四四个先验功能是根据平面两环五粒子振幅所知的五角大楼功能空间表达的,但有趣的是,只有一部分功能出现了。作为四个无量纲变量的函数,可观察到的渐近极限。我们验证了我们的分析结果与软限制和线性限制一致,并在多重量限制中找到一个有趣的简单模式。多亏了新的结果,我们还可以猜想预测,对于一般的运动学,在纯Yang-mills理论中,平面三环五粒子全幅度的最大重量片段。由Amplituhedron几何形状的动机,我们研究了综合答案的阳性特性。在四个粒子上概括了先前的结果,我们发现数值证据表明,两环五粒子结果在环路扩增子建议的运动学区域中具有均匀的符号。
We compute the two-loop result for the null pentagonal Wilson loop with a Lagrangian insertion (normalized by the Wilson loop without insertion) in planar, maximally supersymmetric Yang-Mills theory. This finite observable is closely related to the Amplituhedron, and it is reminiscent of finite parts of planar two-loop five-particle scattering amplitudes. We verify that, up to this loop order, the leading singularities are given by the same conformally invariant expressions that appear in all-plus pure Yang-Mills amplitudes. The accompanying weight-four transcendental functions are expressed in terms of the pentagon functions space known from planar two-loop five-particle amplitudes, but interestingly only a subset of the functions appears. Being a function of four dimensionless variables, the observable has interesting asymptotic limits. We verify that our analytic result is consistent with soft and collinear limits, and find an intriguingly simple pattern in the multi-Regge limit. Thanks to the new result we can also conjecturally predict, for general kinematics, the maximal weight piece of the planar three-loop five-particle all-plus amplitude in pure Yang-Mills theory. Motivated by the Amplituhedron geometry, we investigate positivity properties of the integrated answer. Generalizing previous results at four particles, we find numerical evidence that the two-loop five-particle result has uniform sign in a kinematic region suggested by the loop Amplituhedron.