Non-integrability for $ \mathcal{N}=1 $ SCFTs in $ 5d $

We explore the \emph{Liouvillian} non-integrability criteria for long quiver gauge theories those preserve $\mathcal{N}=1$ SUSY in $5d$. We probe type IIB solutions with (an $AdS_6$ factor) semi-classical strings which capture the strong coupling dynamics of $\mathcal{N}=1$ SCFTs in $5d$. Our analysis reveals an underlying non-integrable structure within some sub-sector of these $5d$ SCFTs. To solidify our claim, we complement our analytic results through numerics. We estimate various chaos indicators for the phase space which confirm the onset of a \emph{chaotic} motion for these type IIB strings.