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

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 halfgeodesics 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.

Chaos and pole-skipping in rotating black holes

“…In addition to the above example, holographic theories also exhibit pole-skipping in the lower-half plane of complex frequency space[22]. These are not directly connected to the form (1.1) of the OTOC, but can still provide interesting constraints on the dispersion relations of the field theory's collective excitations[23][24][25][26][27][28][29][30][31][32][33][34][35].…”