Bouncing singularities and thermal correlators on line defects

TL;DR

This paper investigates bouncing singularities in thermal correlators within holographic conformal field theories, confirming their universal high-frequency structure through multiple analytical methods and extending the analysis to defect operators on Wilson lines.

Contribution

It demonstrates the agreement between WKB and OPE methods in identifying bouncing singularities and extends the analysis to defect correlators, proposing a universal factorization formula.

Findings

Bouncing singularities appear in thermal correlators in AdS black hole backgrounds.

WKB and OPE analyses agree on the presence and structure of these singularities.

Defect correlators on Wilson lines also exhibit bouncing singularities, indicating universality.

Abstract

Thermal correlators in holographic conformal field theories are known to exhibit singularities in complex time, sometimes referred to as ``bouncing singularities", which are believed to be related to bulk geodesics probing the black hole interior. These singularities correspond to exponentially suppressed contributions in the high-frequency limit of the thermal correlators. We revisit in detail the calculation of retarded two-point functions of local operators dual to bulk scalar fields in the planar AdS black hole background. We confirm that these correlators develop bouncing singularities, and highlight the agreement of two independent methods: a large frequency WKB analysis with infalling boundary conditions at the horizon; and an asymptotic OPE analysis that relies only on the near-boundary expansion, without any direct input from the black hole interior. We then extend these calculations to the case of the retarded two-point function of displacement operators on a Wilson line in the finite temperature gauge theory. This is computed holographically by solving the wave equation for the transverse fluctuations of the dual string worldsheet in the planar AdS black hole background. We find that these defect correlators also exhibit bouncing singularities, and again observe exact agreement between the WKB analysis sensitive to the black hole interior and the asymptotic OPE analysis. This agreement suggests that the bouncing singularities and the corresponding OPE data encode a universal high-frequency structure of the retarded correlators, and we propose a factorization formula that encodes the deviations from this universality.