Regge conformal blocks from the Rindler-AdS black hole and the pole-skipping phenomena

TL;DR

This paper constructs holographic conformal blocks in the Regge limit using Rindler-AdS black hole coordinates, revealing their connection to pole-skipping phenomena and late-time Regge behaviors.

Contribution

It generalizes geodesic Witten diagrams to Rindler-AdS black holes and links conformal blocks with pole-skipping through near-horizon analysis.

Findings

Late-time behaviors match Regge limits of conformal blocks

Constructed diagrams with four external scalars in Rindler-AdS

Near-horizon analysis captures Regge behaviors for any integer spin

Abstract

We study a holographic construction of conformal blocks in the Regge limit of four-point scalar correlation functions by using coordinates of the two-sided Rindler-AdS black hole. As a generalization of geodesic Witten diagrams, we construct diagrams with four external scalar fields in the Rindler-AdS black hole by integrating over two half-geodesics between the centers of Penrose diagrams and points at the AdS boundary. We demonstrate that late-time behaviors of the diagrams coincide with the Regge behaviors of conformal blocks. We also point out their relevance with the pole-skipping phenomena by showing that the near-horizon analysis of symmetric traceless fields with any integer spin in the Rindler-AdS black hole can capture the Regge behaviors of conformal blocks.