Integrability and non-integrability for marginal deformations of 4d $\mathcal{N}=2$ SCFTs

We study integrability and non-integrability for marginal deformations of 4d $\mathcal{N}=2$ SCFTs. We estimate various chaos indicators for the bulk theory which clearly shows the onset of a chaotic string dynamics in the limit of large deformations. On the other hand, for small values of the deformation parameter, the resulting dynamics exhibits a non-chaotic motion and therefore presumably an underlying integrable structure. Our analysis reveals that the $\gamma$-deformation in the type-IIA theory could be interpreted as an interpolation between a class of integrable $\mathcal{N}=2$ SCFTs and a class of non-integrable $\mathcal{N}=1$ SCFTs at strong coupling. We also generalise our results in the presence of the flavor branes.