论文标题
如何在不真正尝试的情况下取得成功的Witten图递归
How to Succeed at Witten Diagram Recursions without Really Trying
论文作者
论文摘要
Witten图是研究ADS空间中动力学的基本对象，并且在分析功能引导程序中也起关键作用。但是，众所周知，这些图很难评估，因此很难搜索它们之间的递归关系。在本说明中，我们提出了简单的方法，以获取从共形块递归关系的交换图表的递归关系。我们发现了各种新关系，包括用于交换图表的维度还原公式。特别是，我们找到了五个递归关系，与$ d $和$ d-2 $尺寸相关的交换图。这给出了由于巴西 - 苏拉斯超对称性而引起的相似公式的类似公式的全息类似物。我们还将分析扩展到具有共形边界的CFT中的两点函数，并获得相似的结果。
Witten diagrams are basic objects for studying dynamics in AdS space, and also play key roles in the analytic functional bootstrap. However, these diagrams are notoriously hard to evaluate, making it extremely difficult to search for recursion relations among them. In this note, we present simple methods to obtain recursion relations for exchange Witten diagrams from conformal block recursion relations. We discover a variety of new relations, including the dimensional reduction formulae for exchange Witten diagrams. In particular, we find a five-term recursion relation relating exchange Witten diagrams in $d$ and $d-2$ dimensions. This gives the holographic analogue of a similar formula for conformal blocks due to Parisi-Sourlas supersymmetry. We also extend the analysis to two-point functions in CFTs with conformal boundaries, and obtain similar results.
