We study the analytic structure of loop Witten diagrams in Euclidean AdS represented by their conformal partial wave expansions. We show that, as in flat space, amplitude’s singularities are associated with non-trivial cuts of the diagram and factorize into products of the coefficient functions for the subdiagrams resulting from these cuts. We consider an example of a one-loop four-point diagram in detail and then briefly discuss how the procedure can be extended to more general diagrams. Finally, we show that this analysis reproduces simple relations that follow from the large- N considerations on the boundary.

中文翻译：

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从批量循环到边界大 N 扩展

我们研究了欧几里得 AdS 中回路 Witten 图的解析结构，由它们的共形分波展开表示。我们表明，就像在平坦空间中一样，振幅的奇点与图的非平凡切割相关联，并分解为这些切割产生的子图的系数函数的乘积。我们详细考虑一个单环四点图的例子，然后简要讨论如何将该过程扩展到更一般的图。最后，我们表明该分析再现了从边界上的大 N 考虑得出的简单关系。