Abstract

Higher-point functions of gauge invariant composite operators in \(\mathcal{N} = 4\) super Yang–Mills theory can be computed via triangulation. The elementary tile in this process is the hexagon introduced for the evaluation of structure constants. A gluing procedure welding the tiles back together is needed to return to the original object. We re-analyse previous work on five-point functions of half-BPS operators. At one loop this involves dressing a pentagonal matter skeleton graph by virtual exchanges. There are two types of contributing processes: the gluing of two adjacent tiles by one virtual magnon, and the gluing of three adjacent tiles by two virtual magnons. The latter process is of the utmost interest, because it is the first instance in which virtual particles scatter on a hexagon. While we keep the restricted kinematics used in the original article on the problem, we employ a different “mirror rotation”, thus rendering a large part of the four-variable problem accessible to analytic methods. For the resulting multiple series of hypergeometric type two summation techniques are developed: integration in the modulus, and substitution of the integral representation of \(_{{p + 1}}{{F}_{p}}\) functions. All solvable contributions individually yield hyperlogarithms of weight two.

中文翻译：

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束缚态S矩阵的对数

摘要

\（\ mathcal {N} = 4 \）中的规范不变复合算子的高点函数超级杨米尔斯理论可以通过三角剖分来计算。此过程中的基本图块是为评估结构常数而引入的六边形。需要用胶合程序将瓷砖焊接在一起，以返回到原始对象。我们重新分析了以前关于半BPS运营商的五点功能的工作。在一个循环中，这涉及通过虚拟交换来修饰五边形物质骨架图。贡献过程有两种类型：一个虚拟马农粘在一起的两个相邻的瓷砖，和两个虚拟马农粘在一起的三个相邻的瓷砖。后一个过程具有最大的意义，因为它是虚拟粒子在六边形上散射的第一个实例。虽然我们保留了该问题上原始文章中使用的受限运动学，但我们采用了不同的“镜像旋转”，因此，四变量问题的很大一部分可供分析方法使用。对于所得的多个超几何类型系列，开发了两种求和技术：模中的积分，以及的积分表示的替代。\（_ {{p + 1}} {{F} _ {p}} \）函数。所有可解贡献分别产生权重为2的超对数。