A Stochasticity Threshold in Holography and and the Instability of AdS

Abstract

We give strong numerical evidence that a self-interacting probe scalar field in AdS, with only a few modes turned on initially, will undergo fast thermalization only if it is above a certain energetic threshold. Below the threshold the energy stays close to constant in a few modes for a very long time instead of cascading quickly. This indicates the existance of a Strong Stochasticity Threshold (SST) in holography. The idea of SST is familiar from certain statistical mechanical systems, and we suggest that it exists also in AdS gravity. This would naturally reconcile the generic non-linear instability of AdS observed by Bizon and Rostworowski, with the Fermi-Pasta-Ulam-Tsingou-like quasi-periodocity noticed recently for some classes of initial conditions. We show that our simple set-up captures many of the relevant features of the full gravity-scalar system.

arXiv comment12 pages, 6 figures

References in corpus (5)

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• Holographic Thermalization, stability of AdS, and the Fermi-Pasta-Ulam-Tsingou paradox
• Renormalization group, secular term resummation and AdS (in)stability
• Is AdS stable?
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