论文标题
联邦相关器的广告和S型图中的Landau图
Landau diagrams in AdS and S-matrices from conformal correlators
论文作者
论文摘要
ADS中的量子场理论在边界上产生共形相关函数，而在AD几乎是平面的极限下，应该能够从此类相关器中提取S-Matrix。我们讨论了一个特别简单的位置空间程序。它具有从边界位置到（壳上）动量的直接地图，从而将交叉比率与曼德尔斯坦不变式相关联。该食谱在几个示例中取得了成功，包括势头支持的三角洲功能，可以证明意味着基于梅林空间和OPE数据，在Arxiv：1607.06109中的两个建议。有趣的是，该过程并不总是可行的：Feynman图的Landau奇异性被证明是较大区域的一部分，被称为“不良区域”，其中Witten图的扁平空间极限差异。为了捕获这些差异，我们介绍了广告中Landau图的概念。就像在平坦的空间中一样，它们描述了在复杂空间中大距离传播的壳颗粒，并具有在每个散装顶点保持动量保护的形式。作为应用程序，我们恢复了不良区域边界上四点三角图的异常阈值。
Quantum field theories in AdS generate conformal correlation functions on the boundary, and in the limit where AdS is nearly flat one should be able to extract an S-matrix from such correlators. We discuss a particularly simple position-space procedure to do so. It features a direct map from boundary positions to (on-shell) momenta and thereby relates cross ratios to Mandelstam invariants. This recipe succeeds in several examples, includes the momentum-conserving delta functions, and can be shown to imply the two proposals in arXiv:1607.06109 based on Mellin space and on the OPE data. Interestingly the procedure does not always work: the Landau singularities of a Feynman diagram are shown to be part of larger regions, to be called `bad regions', where the flat-space limit of the Witten diagram diverges. To capture these divergences we introduce the notion of Landau diagrams in AdS. As in flat space, these describe on-shell particles propagating over large distances in a complexified space, with a form of momentum conservation holding at each bulk vertex. As an application we recover the anomalous threshold of the four-point triangle diagram at the boundary of a bad region.
