Hexagonalization of correlation functions
Hexagonalization of correlation functions
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相关函数的六角化
DOI：
10.1007/jhep01(2017)130
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发表时间：
2016
影响因子：
5.4
通讯作者：
S. Komatsu
中科院分区：
文献类型：
--
作者：
T. Fleury;S. Komatsu
我们提出了一个非微扰框架来研究N-Documentclass[12pt]{Minimum}\usepackage{amsath}\usepackage{wa ysym}\usepackage{amsfonts}\usepackage{amsbsy}\usepackage{matrsfs}\usepackage{upgreek}\setlong{\oddsidemarin}{-69pt}\Begin{Document}$$\End{Document}=4超对称Yang-Mills理论中的一般相关函数。基本策略是将它们分解成称为六边形形状因子的基本构建块，早些时候引入六边形形状因子是为了利用可积性来研究结构常数。这种分解类似于黎曼曲面的三角剖分，因此我们称之为六角化。我们提出了一套基于对称性将六边形粘合在一起的规则，该规则自然地包含了对共形和R对称交叉比的依赖。我们的方法在概念上不同于传统的算子乘积扩展，并且自动考虑了OPE通道中交换的多道算子。为了在简单的设置中说明这一思想，我们计算了任意长度的BPS算子的四点函数以及一个Konishi算子和三个短BPS算子的关联函数，全部在一个循环中。在所有情况下，结果都与摄动数据完全一致。我们还建议，我们的方法可以成为研究共形积分的有用工具，并在阶梯积分的情况下明确地展示了它。
We propose a nonperturbative framework to study general correlation functions of single-trace operators in N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 4 supersymmetric Yang-Mills theory at large N . The basic strategy is to decompose them into fundamental building blocks called the hexagon form factors, which were introduced earlier to study structure constants using integrability. The decomposition is akin to a triangulation of a Riemann surface, and we thus call it hexagonalization. We propose a set of rules to glue the hexagons together based on symmetry, which naturally incorporate the dependence on the conformal and the R-symmetry cross ratios. Our method is conceptually different from the conventional operator product expansion and automatically takes into account multi-trace operators exchanged in OPE channels. To illustrate the idea in simple set-ups, we compute four-point functions of BPS operators of arbitrary lengths and correlation functions of one Konishi operator and three short BPS operators, all at one loop. In all cases, the results are in perfect agreement with the perturbative data. We also suggest that our method can be a useful tool to study conformal integrals, and show it explicitly for the case of ladder integrals.
AdS/CFT 可集成性回顾：概述
影响因子：
1.2
作者：
Beisert N
通讯作者：
Beisert N