论文标题
$ \ MATHCAL {N} = 4 $ SUPER YANG-MILLS和时期的集成相关器
Integrated correlators in $\mathcal{N}=4$ super Yang-Mills and periods
论文作者
论文摘要
我们研究了$ \ Mathcal {n} = 4 $ supersymmetricric的Yang-mills，使用标准Feynman图计算，研究了最近提出的最近提议的集成四点相关器的扰动方面。我们认为，综合相关器的扰动贡献是由某些保形的Feynman图周期的线性组合给出的，该图最初是为了构建未集成相关器的扰动循环积分的引入。该观察结果使我们能够评估综合相关器对高循环订单。我们明确计算一个在平面极限内最多四个循环的集成相关器之一，对于另一个集成的相关器，最多三个循环，并找到与从超对称定位获得的结果一致。综合相关器与某些时期之间的识别也意味着这些时期之间的非平凡关系，因为人们可以使用本地化计算综合相关器。我们通过在平面限制中以五个循环的方式考虑一个集成相关器之一来说明这一想法，在该循环中，本地化结果导致对特定六环积分期间的预测。
We study perturbative aspects of recently proposed integrated four-point correlators in $\mathcal{N}=4$ supersymmetric Yang-Mills with all classical gauge groups using standard Feynman diagram computations. We argue that perturbative contributions of the integrated correlators are given by linear combinations of periods of certain conformal Feynman graphs, which were originally introduced for the construction of perturbative loop integrands of the un-integrated correlator. This observation allows us to evaluate the integrated correlators to high loop orders. We explicitly compute one of the integrated correlators up to four loops in the planar limit, and up to three loops for the other integrated correlator, and find agreement with the results obtained from supersymmetric localisation. The identification between the integrated correlators and certain periods also implies non-trivial relations among these periods, given that one may compute the integrated correlators using localisation. We illustrate this idea by considering one of the integrated correlators at five loops in the planar limit, where the localisation result leads to a prediction for the period of a certain six-loop integral.
