Chaos in classical string dynamics in $\hat{\gamma}$ deformed $AdS_5 \times T^{1,1}$

TL;DR

This paper investigates chaos in classical string dynamics within a deformed $AdS_5 imes T^{1,1}$ background, demonstrating non-integrability and analyzing how chaos depends on energy and deformation parameters.

Contribution

It reveals chaotic behavior in extended strings in $ ilde{eta}$-deformed backgrounds and distinguishes it from non-chaotic point-like objects, providing Lyapunov exponents as quantitative measures.

Findings

Chaotic phase space behavior for extended strings.

Non-chaotic behavior for point-like objects.

Lyapunov exponents confirm chaos in extended strings.

Abstract

We consider a circular string in $\hat{\gamma}$ deformed $AdS_5 \times T^{1,1}$ which is localized in the center of $AdS_5$ and winds around the two circles of deformed $T^{1,1}$. We observe chaos in the phase space of the circular string implying non-integrability of string dynamics. The chaotic behaviour in phase space is controlled by energy as well as the deforming parameter $\hat{\gamma}$. We further show that the point like object exhibits non-chaotic behaviour. Finally we calculate the Lyapunov exponent for both extended and point like object in support of our first result.