Wormholes and out-of-time ordered correlators in gauge/gravity duality

TL;DR

This paper investigates the chaotic behavior and scrambling dynamics of traversable wormholes in AdS/CFT, revealing regimes of fast and slow scrambling with implications for wormhole teleportation and holographic duality.

Contribution

It provides a detailed analysis of out-of-time ordered correlators in wormhole backgrounds, highlighting different scrambling regimes and their holographic dual interpretations.

Findings

Fast scrambling saturates MSS bound in short-lived wormholes

Long-lived wormholes exhibit exponential slowdown of scrambling

Results relate to SYK model and wormhole teleportation limitations

Abstract

We calculate the four-wave scattering amplitude in the background of an AdS traversable wormhole in 2+1 dimensions created by a nonlocal coupling of AdS boundaries in the BTZ black hole background. The holographic dual of this setup is a pair of CFTs coupled via a double-trace deformation, the scattering amplitude giving the out-of-time ordered correlator (OTOC) in CFT. Short-living wormholes always exhibit a regime of fast scrambling, saturating the MSS bound for the Lyapunov exponent but in the early-time regime the scrambling can be slower, with a Lyapunov exponent linear in $T$ but below the MSS bound. For long-living (near-eternal) wormholes however the numerics suggests the existence of another regime, with a drastic (exponential) slowdown of scrambling and an exponentially small Lyapunov exponent. Our findings have parallels in the SYK model, and may indicate certain limitations of wormhole teleportation protocols previously studied in the literature.