Non-chaotic dynamics for Yang-Baxter deformed ${\text{AdS}}_4\times {\text{CP}}^3$ superstrings

We explore a novel class of Yang-Baxter deformed AdS${}_4$ $\times$ CP${}^3$ backgrounds [Jour. High Ener. Phys. $\mathbf{\text{01}}$ (2021) 056] which exhibit a non-chaotic dynamics for (super)strings propagating over it. We explicitly use the $\mathit{\text{Kovacic’s}}\mathit{\text{algorithm}}$ 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 Poincaré 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.