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

TL;DR

This paper investigates the pole-skipping phenomena in thermal two-point functions of scalar and vector fields in hyperbolic space within conformal field theories, revealing their connection to conformal blocks and holography.

Contribution

It derives the pole-skipping points using multiple methods and links these points to the late-time behavior of conformal blocks in four-point out-of-time-order correlators.

Findings

Confirmed pole-skipping points via three different methods.

Established the relation between pole-skipping and conformal block behavior.

Connected pole-skipping phenomena with holographic and field theoretic frameworks.

Abstract

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.