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arXiv · 1505.07583

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

Yuhma Asano·Daisuke Kawai·Hideki Kyono·Kentaroh Yoshida
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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.

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Yuhma Asano, Daisuke Kawai, Hideki Kyono, Kentaroh Yoshida. 2015-05-28. Chaotic strings in a near Penrose limit of AdS$_5\times T^{1,1}$. https://doi.org/10.1007/jhep08(2015)060

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