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 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.

Chaos and pole-skipping in rotating black holes

“…In this paper, our goal is to study the relationship between many-body quantum chaos and energy dynamics for an example dual to a higher-dimensional rotating black hole, 1 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].…”

Construction of bulk solutions for towers of pole-skipping points

“…. , h r...r ) because they are expected to give the leading special points [9,10,13], and it really does in our case [44]. However, the other components of fields (i.e., h v...vi , h v...vij , .…”

“…In the study of the pole-skipping phenomena, the leading special points of gravitons have been found at iω = −2πT [6]. On the Rindler-AdS black hole, the leading special points of spin-fields were found at iω = 2π(1 − )T [44], and the towers of special points (2.55) at iω = 2π(n + 1 − )T seem to be present from the analysis in Section 2. If these special points of spin-fields in the black hole (3.19) also exist at iω = 2π(n + 1 − )T , the integrals (4.12) capture the behaviors at these special points.…”

“…starting from the leading special points as we did in the vector field case even though the equations are complicatedly coupled differential equations. The leading special points of symmetric traceless rank-tensor fields were first determined by this method in [44]:…”

“…where the leading special points (n = 0) are revealed in [44] for general integer . Exponential behaviors at the large d limit corresponding to these inferred results are e 2πT ( −n−1)v e −µd , µ = (∆ − n + 2q − 1)…”