Abstract
We study chaotic motions of a classical string in a near Penrose limit of AdS5 × T 1,1. It is known that chaotic solutions appear on R ×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 KolmogorovArnold-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 Poincaré sections. In comparison to the AdS5 ×T 1,1 case, we argue that no chaos lives in a near Penrose limit of AdS5×S5, as expected from the classical integrability of the parent system.
Highlights
Be nice to consider a gravitational interpretation of the chaotic behavior of D0-branes
We study chaotic motions of a classical string in a near Penrose limit of AdS5 × T 1,1
The AdS5 × T 1,1 background is obtained as the near-horizon limit of a stack of N D3-branes sitting at the tip of the conifold and the resulting geometry is considered as the gravity dual for an N = 1 superconformal field theory in four dimensions [31]
Summary
We will derive the light-cone Hamiltonian of a string moving on the near pp-wave background (2.7). Our derivation follows the procedure developed in [38, 39] for the AdS5×S5 case, though we employ only the bosonic part. We first work on a general background and solve the constraint conditions. The metric (2.7) is substituted into the resulting expression and the light-cone Hamiltonian we consider is derived
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