Motivated by the recent connection between pole-skipping phenomena of two point functions and four point out-of-time-order correlators (OTOCs), we study the pole structure of thermal two-point functions in $d$-dimensional conformal field theories (CFTs) in hyperbolic space. We derive the pole-skipping points of two-point functions of scalar and vector fields by three methods (one field theoretic and two holographic methods) and confirm that they agree. We show that the leading pole-skipping point of two point functions is related with the late time behavior of conformal blocks and shadow conformal blocks in four-point OTOCs.

中文翻译：

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双曲空间中标量场和矢量场的极点跳跃：共形块和全息术

受最近两点函数的极点跳跃现象与四点无序相关器 (OTOC) 之间的联系的启发，我们研究了 $d$ 维共形场理论中热两点函数的极点结构（ CFT）在双曲空间中。我们通过三种方法（一种场论和两种全息方法）推导出标量场和矢量场的两点函数的极点跳跃点，并确认它们是一致的。我们表明，两点函数的领先跳极点与四点 OTOC 中保形块和阴影保形块的后期行为有关。