Bulkcone Singularities and Complex Geodesics

TL;DR

This paper explores the nature of bulk-cone singularities in holographic CFTs, revealing their connection to complex null geodesics and phase transitions between real and complex geodesics.

Contribution

It introduces the concept of complex null geodesics as the origin of spacelike singularities in thermal CFT correlators and analyzes the phase transition between different geodesic types.

Findings

Bulk-cone singularities are linked to complex null geodesics.

A phase transition exists between real and complex spacelike geodesics.

Phase-shift calculations determine the position of these singularities.

Abstract

Thermal correlators in holographic CFTs on a sphere exhibit bulk-cone singularities at points connected by null geodesics in the bulk. The operator product expansion analysis of the stress-tensor sector of the correlator shows that there are analogous singularities at spacelike separation for thermal CFTs on a plane. We show that these are associated with complex null geodesics. There is a phase transition between the real and complex spacelike geodesics underpinning this picture. We also provide a phase-shift calculation of the position of these generalised bulk-cone singularities.