Neumann boundary conditions in anti-de Sitter space admit non-collapsing, multi-mode scalar solutions with arbitrarily small amplitude despite a fully resonant spectrum.
Charting the AdS Islands of Stability with Multi-oscillators?
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abstract
We propose the existence of an infinite-parameter family of solutions in AdS that oscillate on any number of non-commensurate frequencies. Some of these solutions appear stable when perturbed, and we suggest that they can be used to map out the AdS "islands of stability". By numerically constructing two-frequency solutions and exploring their parameter space, we find that both collapse and non-collapse are generic scenarios near AdS. Unlike other approaches, our results are valid on any timescale and do not rely on perturbation theory.
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New islands of stability with double-trace deformations
Neumann boundary conditions in anti-de Sitter space admit non-collapsing, multi-mode scalar solutions with arbitrarily small amplitude despite a fully resonant spectrum.