Bulkcone Singularities and Complex Geodesics

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.