Bouncing off a stringy singularity

TL;DR

The paper investigates how stringy corrections at finite coupling modify the holographic signatures of black hole singularities in thermal boundary correlators. By linking bouncing geodesics to quasinormal modes and analyzing the complex-time structure via the SYK model at infinite temperature, it shows that the sharp singularities shift off the real time sections into the complex plane, forming finite-height bumps. It also analyzes the impact of zeroes and multiple QNM families, finding that zeroes can destroy the lattice structure while higher-q SYK data reveal a finite-coupling smoothing consistent with stringy geometry. The results support a bulk picture in which planar theories at finite coupling resemble stringy black holes and motivate further exploration of finite-coupling effects in higher-dimensional holography and related melonic theories.

Abstract

A sharp signature of the black hole singularity in holography is a divergence in the boundary thermal two-point function at a specific point in the complex time plane. This divergence arises from a null geodesic that bounces off the black hole singularity. At finite 't Hooft coupling, stringy corrections to the bulk dynamics cannot be neglected, and the fate of the bouncing geodesic is an open question. We propose a simple scenario in which the singularity in the two-point function is shifted slightly into the complex plane, thereby smoothing it out into a finite-size bump. We demonstrate this smoothing explicitly in a microscopic example, namely the Sachdev-Ye-Kitaev model at infinite temperature, where the correlator is under analytic control. Our result suggests a bulk description of planar theories at finite coupling as stringy black holes.

Figures (9)

• Figure 1: (a) A bouncing geodesic in the maximally extended $\text{AdS}_5$-Schwarzschild black brane. In order for the geodesic to meet the singularity at the center of the diagram it must start with boundary time $t=-\frac{\beta}{4}<0$. (b) A bouncing worldsheet in string theory.
• Figure 2: Lattice of singular points of $C(t)$ in complex time, with real sections shown as dashed lines. The black dots denote singularities at the lattice points (\ref{['latticedef']}), while the red arrows are the vectors generating the lattice. In the lower half plane there are singularities at $t=-t_{nm}$.
• Figure 3: Lattice of singular points of $C(t)$ in the presence of a purely imaginary line of QNMs, in addition to the complex line considered previously. All singularities fall on the real sections $\text{Im }t=n\beta/2+m\beta_{\text{in}}/2$. To avoid clutter we only plot the real sections $\text{Im }t=n\beta/2$ and $\text{Im }t=\beta/2+n(\beta-\beta_{\text{in}})/2$, shown in dashed gray and dashed brown respectively.
• Figure 4: A bouncing geodesic in the maximally extended Reissner-Nordström-AdS black brane. Similarly to what happens in the uncharged case, in order for the geodesic to meet the singularity at $\text{Re }t=0$, it must start with boundary time $t<0$. In contrast to the case of a spacelike singularity, every bouncing geodesic that connects two boundaries must cross an inner horizon (shown in brown).
• Figure 5: Singularities of $C(t)$ for the toy model (\ref{['eq:ProductWZeroes']}) with a line of zeroes. Each singularity splits into two points separated by a distance $\alpha'$ in the presence of the zeroes. The real sections $\text{Im }t=n\beta/2$ are depicted as dashed lines.