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

Pole-skipping of scalar and vector fields in hyperbolic space: conformal blocks and holography