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

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 Poincaré sections and Lyapunov spectra for some initial conditions.

arXiv comment13 pages, 3 figures

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• Integrability and non-integrability for holographic dual of Matrix model and non-Abelian T-dual of AdS${}_5\times$S${}^5$
• Chaotic string dynamics in Bosonic $\eta$-deformed $Ad{S}_5\times T^{1,1}$ background
• Turbulence on open string worldsheets under non-integrable boundary conditions