Chaotic string dynamics in deformed $T^{1,1}$

TL;DR

This paper demonstrates that the classical string dynamics in a deformed $T^{1,1}$ background exhibit chaos, confirming the non-integrability of the system when the Kalb-Ramond two-form is off critical value.

Contribution

The authors explicitly show classical chaos in the deformed $T^{1,1}$ sigma model, providing evidence for non-integrability beyond the critical two-form value.

Findings

Classical chaos confirmed via Poincaré sections.

Lyapunov spectra indicate non-integrability.

Chaos appears when the two-form is off critical value.

Abstract

Recently, Arutyunov, Bassi and Lacroix have shown that 2D non-linear sigma model with a deformed $T^{1,1}$ background is classically integrable [arXiv:2010.05573 [hep-th]]. This background includes a Kalb-Ramond two-form with a critical value. Then the sigma model has been conjectured to be non-integrable when the two-form is off critical. We confirm this conjecure by explicitly presenting classical chaos. With a winding string ansatz, the system is reduced to a dynamical system described by a set of ordinary differential equations. Then we find classical chaos, which indicates non-integrability, by numerically computing Poincar\'{e} sections and Lyapunov spectra for some initial conditions.