Chaos around Holographic Regge Trajectories

TL;DR

This paper demonstrates that the classical spinning string solutions dual to Regge trajectories in confining holographic backgrounds exhibit non-integrability and chaos, confirmed through analytical and numerical methods across various supergravity models.

Contribution

It analytically proves non-integrability of the dynamical system associated with holographic Regge trajectories and confirms chaotic behavior numerically in multiple supergravity backgrounds.

Findings

The system is non-integrable in general confining backgrounds.

Holographic Regge trajectories form an integrable island in phase space.

Strings exhibit chaotic motion confirmed by Lyapunov exponents and Poincare sections.

Abstract

Using methods of Hamiltonian dynamical systems, we show analytically that a dynamical system connected to the classical spinning string solution holographically dual to the principal Regge trajectory is non-integrable. The Regge trajectories themselves form an integrable island in the total phase space of the dynamical system. Our argument applies to any gravity background dual to confining field theories and we verify it explicitly in various supergravity backgrounds: Klebanov-Strassler, Maldacena-Nunez, Witten QCD and the AdS soliton. Having established non-integrability for this general class of supergravity backgrounds, we show explicitly by direct computation of the Poincare sections and the largest Lyapunov exponent, that such strings have chaotic motion.