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We calculate the four-wave scattering amplitude in the background of an AdStraversable wormhole in 2+1 dimensions created by a nonlocal coupling of AdSboundaries in the BTZ black hole background. The holographic dual of this setupis a pair of CFTs coupled via a double-trace deformation, the scatteringamplitude giving the out-of-time ordered correlator (OTOC) in CFT. Short-livingwormholes always exhibit a regime of fast scrambling, saturating the MSS boundfor the Lyapunov exponent but in the early-time regime the scrambling can beslower, with a Lyapunov exponent linear in $T$ but below the MSS bound. Forlong-living (near-eternal) wormholes however the numerics suggests theexistence of another regime, with a drastic (exponential) slowdown ofscrambling and an exponentially small Lyapunov exponent. Our findings haveparallels in the SYK model, and may indicate certain limitations of wormholeteleportation protocols previously studied in the literature.

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