Non-chaotic dynamics for Yang-Baxter deformed $\text{AdS}_{4}\times \text{CP}^{3}$ superstrings

TL;DR

This paper investigates a class of Yang-Baxter deformed AdS4 x CP3 backgrounds and demonstrates, through analytical and numerical methods, that string dynamics on these backgrounds are non-chaotic, suggesting non-integrability but not full integrability.

Contribution

It introduces a novel analysis combining Kovacic's algorithm and numerical chaos indicators to study string dynamics on deformed backgrounds, excluding non-integrability.

Findings

String dynamics are non-chaotic on these backgrounds.

Numerical chaos indicators support analytical results.

Analysis suggests non-integrability but not full integrability.

Abstract

We explore a novel class of Yang-Baxter deformed AdS$_{4}$ $\times$ CP$^{3}$ backgrounds [Jour. High Ener. Phys. \textbf{01} (2021) 056] which exhibit a non-chaotic dynamics for (super)strings propagating over it. We explicitly use the \textit{Kovacic's algorithm} in order to establish non-chaotic dynamics of string $ \sigma $ models over these deformed backgrounds. This analysis is complemented with numerical techniques whereby we probe the classical phase space of these (semi)classical strings and calculate various chaos indicators, such as, the Poincar\'{e} sections and the Lyapunov exponents. We find compatibility between the two approaches. Nevertheless, our analysis does not ensure integrability; rather, it excludes the possibility of non-integrability for the given string embeddings.