Chaotic string motion in a near pp-wave limit

TL;DR

This paper investigates classical string dynamics in a near pp-wave limit of AdS5×S5, revealing that truncating the exponential potential leads to non-integrable, chaotic behavior similar to the Henon-Heiles system.

Contribution

It demonstrates that string motion in a near pp-wave limit can become chaotic due to potential truncation, connecting string dynamics to well-known non-integrable models.

Findings

String motion becomes chaotic when the exponential potential is truncated.

The system transitions from integrable to non-integrable behavior.

Chaotic dynamics are analogous to the Henon-Heiles model.

Abstract

We revisit classical string motion in a near pp-wave limit of AdS$_5\times$S$^5$. It is known that the Toda lattice models are integrable. But if the exponential potential is truncated at finite order, then the system may become non-integrable. In particular, when the exponential potential in a three-particle periodic Toda chain is truncated at the third order of the dynamical variables, the resulting system becomes a well-known non-integrable system, Henon-Heiles model. The same thing may happen in a near pp-wave limit of AdS$_5\times$S$^5$, on which the classical string motion becomes chaotic.