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P. Henrici, Applied and computational complex analysis
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2015

Ultraviolet asymptotics for quasiperiodic AdS_4 perturbations

Craps, Ben, Evnin, Oleg, Jai-akson, Puttarak et al.

Understand

Spherically symmetric perturbations in AdS-scalar field systems of small amplitude epsilon approximately periodic on time scales of order 1/epsilon^2 (in the sense that no significant transfer of energy between the AdS normal modes occurs) have played an important role in considerations of AdS stability.

They are seen as anchors of stability islands where collapse of small perturbations to black holes does not occur.
(This collapse, if it happens, typically develops on time scales of the order 1/epsilon^2.) We construct an analytic treatment of the frequency spectra of such quasiperiodic perturbations, paying special attention to the large frequency asymptotics.
For the case of a self-interacting phi^4 scalar field in a non-dynamical AdS background, we arrive at a fairly complete analytic picture involving quasiperiodic spectra with an exponential suppression modulated by a power law at large mode numbers.