Bulk Phase Shift and Singularity

TL;DR

This paper explores how bulk phase shifts and singularities in holographic CFT correlators relate to high-energy black hole scattering, providing a new way to interpret inelastic effects and geometric quantities.

Contribution

It extends the understanding of bulk phase shifts and their holographic interpretation to small impact parameters, linking singularities in position-space correlators to null geodesics reflecting off black hole singularities.

Findings

Position-space correlator singularities occur at null geodesic reflections.

Inelastic scattering introduces imaginary parts to phase shifts.

Bulk-cone singularities provide a robust probe of black hole geometry.

Abstract

High-energy scattering of a light particle off a black hole at fixed impact parameter is described by an eikonal phase, which encodes the resulting time delay and angular deflection. This bulk phase shift admits a holographic interpretation as of the thermal momentum-space two-point function of a scalar operator in the CFT in the Regge limit. At small impact parameter, the phase shift acquires an imaginary part signaling inelastic scattering, obscuring the interpretation of time delay and deflection which become complex-valued. However, in a holographic CFT these quantities can also be extracted from the so called bulk-cone singularities of the position space thermal correlator. Extending this analysis to small impact parameters, we find that the position-space correlator develops a singularity precisely when a null geodesic reflects off the black hole singularity and reaches the opposite boundary. This provides a more robust identification of bulk time delay and angular deflection through singularities of position-space correlators.