Chaotic strings in a near Penrose limit of AdS${}_5\times T^{1,1}$

Abstract

We study chaotic motions of a classical string in a near Penrose limit of AdS${}_5\times T^{1,1}$. It is known that chaotic solutions appear on $R\times T^{1,1}$, depending on initial conditions. It may be interesting to ask whether the chaos persists even in Penrose limits or not. In this paper, we show that sub-leading corrections in a Penrose limit provide an unstable separatrix, so that chaotic motions are generated as a consequence of collapsed Kolmogorov-Arnold-Moser (KAM) tori. Our analysis is based on deriving a reduced system composed of two degrees of freedom by supposing a winding string ansatz. Then, we provide support for the existence of chaos by computing Poincare sections. In comparison to the AdS${}_5\times T^{1,1}$ case, we argue that no chaos lives in a near Penrose limit of AdS${}_5\times$S${}^5$, as expected from the classical integrability of the parent system.

19 pages, 9 figures, LaTeX, v2: typos corrected and some clarifications added

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