Interplay of magnetic field and chemical potential induced anisotropy and frame dependent chaos of a $Q\bar{Q}$ pair in holographic QCD

Abstract: We investigate the role of both magnetic field and chemical potential on the emergence of chaotic dynamics in the QCD confining string from the holographic principle. An earlier developed bottom-up model of Einstein-Maxwell-dilaton gravity, which mimics QCD features quite well, is used. The qualitative information about the chaos is obtained using the Poincar\'{e} sections and Lyapunov exponents. We find signatures of chaos in energetically disfavored string configurations, that are closer to the horizon, whereas no chaos is observed in energetically favored string configurations that are away from the horizon. Our results depend quite strongly on the frame we consider in the analysis. In the string frame, the chemical potential and the magnetic field suppress the chaotic dynamics in both parallel and perpendicular orientations of the string with respect to the magnetic field. Meanwhile, in the Einstein frame, the magnetic field suppresses/enhances the chaotic dynamics when the string is orientated perpendicular/parallel to the magnetic field, while the chemical potential enhances the chaotic dynamics for both orientations. The reported Lyapunov exponents are consistent with a classical analogue of the MSS bound in the parameter space of the model and we find it to be always satisfied in both frames.