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

TL;DR

This paper investigates whether chaotic string motions in AdS$_5\times T^{1,1}$ persist under a near Penrose limit, finding that chaos emerges due to sub-leading corrections, unlike the integrable AdS$_5\times S^5$ case.

Contribution

It demonstrates that sub-leading corrections in a near Penrose limit induce chaos in string dynamics on AdS$_5\times T^{1,1}$, contrasting with the integrable AdS$_5\times S^5$ system.

Findings

Chaotic motions appear due to collapsed KAM tori in the near Penrose limit.

Chaos persists in AdS$_5\times T^{1,1}$ but not in AdS$_5\times S^5$.

Poincaré sections support the existence of chaos in the studied system.

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.