# Black Holes, Heavy States, Phase Shift and Anomalous Dimensions

## TL;DR

This paper calculates the phase shift of high-energy particles near AdS black holes and relates it to anomalous dimensions in the dual CFT, confirming results through holographic and gravity calculations across dimensions.

## Contribution

It provides a holographic computation of the phase shift in arbitrary dimensions and links it to anomalous dimensions of double trace operators, extending previous two-dimensional results.

## Key findings

- Agreement between holographic CFT calculations and gravity results.
- Leading order phase shift relates to anomalous dimensions of double trace operators.
- Validation of the phase shift expansion through second-order gravity calculations.

## Abstract

We compute the phase shift of a highly energetic particle traveling in the background of an asymptotically AdS black hole. In the dual CFT, the phase shift is related to a four point function in the Regge limit. The black hole mass is translated to the ratio between the conformal dimension of a heavy operator and the central charge. This ratio serves as a useful expansion parameter; its power measures the number of stress tensors appearing in the intermediate channel. We compute the leading term in the phase shift in a holographic CFT of arbitrary dimensionality using Conformal Regge Theory and observe complete agreement with the gravity result. In a two-dimensional CFT with a large central charge the heavy-heavy-light-light Virasoro vacuum block reproduces the gravity phase shift to all orders in the expansion parameter. We show that the leading order phase shift is related to the anomalous dimensions of certain double trace operators and verify this agreement using known results for the latter. We also perform a separate gravity calculation of these anomalous dimensions to second order in the expansion parameter and compare with the phase shift expansion.