Examining Instabilities Due to Driven Scalars in AdS
arXiv:1912.07143 · doi:10.1007/JHEP12(2020)013
Abstract
We extend the study of the non-linear perturbative theory of weakly turbulent energy cascades in AdS to include solutions of driven systems, i.e. those with time-dependent sources on the AdS boundary. This necessitates the activation of non-normalizable modes in the linear solution for the massive bulk scalar field, which couple to the metric and normalizable scalar modes. We determine analytic expressions for secular terms in the renormalization flow equations for any mass, and for various driving functions. Finally, we numerically evaluate these sources for and discuss what role these driven solutions play in the perturbative stability of AdS.
arXiv commentv1: 29 pages, 6 figures v2: Added reference and small changes to Discussion. 30 pages, 6 figures v3: To appear in JHEP. Added holographic interpretation, review of resummation procedure, and moved discussion of all-normalizable resonances to appendix. 34 pages, 6 figures
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