Conformal Flow on S3 and Weak Field Integrability in AdS4 View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2017-08

AUTHORS

Piotr Bizoń, Ben Craps, Oleg Evnin, Dominika Hunik, Vincent Luyten, Maciej Maliborski

ABSTRACT

We consider the conformally invariant cubic wave equation on the Einstein cylinder R×S3 for small rotationally symmetric initial data. This simple equation captures many key challenges of nonlinear wave dynamics in confining geometries, while a conformal transformation relates it to a self-interacting conformally coupled scalar in four-dimensional anti-de Sitter spacetime (AdS4) and connects it to various questions of AdS stability. We construct an effective infinite-dimensional time-averaged dynamical system accurately approximating the original equation in the weak field regime. It turns out that this effective system, which we call the conformal flow, exhibits some remarkable features, such as low-dimensional invariant subspaces, a wealth of stationary states (for which energy does not flow between the modes), as well as solutions with nontrivial exactly periodic energy flows. Based on these observations and close parallels to the cubic Szegő equation, which was shown by Gérard and Grellier to be Lax-integrable, it is tempting to conjecture that the conformal flow and the corresponding weak field dynamics in AdS4 are integrable as well. More... »

PAGES

1179-1199

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URI

http://scigraph.springernature.com/pub.10.1007/s00220-017-2896-8

DOI

http://dx.doi.org/10.1007/s00220-017-2896-8

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https://app.dimensions.ai/details/publication/pub.1085459493


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