Ramp and plateau in bulk correlators within the disk topology in JT gravity
Cristiano Germani, Mickael Komendyak
TL;DR
This work demonstrates that the dip–ramp–plateau behavior characteristic of chaotic quantum systems and linked to information recovery in black holes can be captured entirely within JT gravity on the disk by evaluating the Hadamard function with a next-to-leading-order steepest-descent expansion of the Schwarzian boundary path integral. The key finding is that correlators spanning the two disconnected black hole exteriors (LR) acquire a linear ramp and a late-time plateau at order $oldsymbol{ u^2}$, while same-side (LL) correlators continue to decay exponentially. Boundary (AdS/CFT) analysis confirms that the cross-boundary correlators exhibit the ramp–plateau structure and that the dip-time scales linearly with $eta$ (i.e., inversely with temperature), consistent with random-matrix predictions. Importantly, these results arise without invoking topology changes or nonperturbative bulk saddles, suggesting that essential information-flow features of the information paradox can be understood from perturbations around a single Lorentzian black hole saddle within disk topology.
Abstract
We show that the solution of the information paradox in Jackiw-Teitelboim gravity - manifested as a linear growth (ramp) followed by saturation (plateau) of matter correlators after an initial decay - is fully encoded in the next-to-leading-order steepest-descent approximation of the gravitational path integral. The correlators exhibiting this ramp-plateau behavior are those entangling the two sides of the eternal black hole, while those on the same side only show an exponential decay. This seems to imply that the information flows across the separate universes that are causally disconnected by the black hole horizon. Finally, we show that the dip-time, defined as the minimum of the correlator, grows inversely with the black hole temperature, as predicted by the holographic dual theory.