Collective modes of polarizable holographic media in magnetic fields

We consider a neutral holographic plasma with dynamical electromagnetic interactions in a finite external magnetic field. The Coulomb interactions are introduced via mixed boundary conditions for the Maxwell gauge field. The collective modes at finite wave-vector are analyzed in detail and compared to the magneto-hydrodynamics results valid only at small magnetic fields. Surprisingly, at large magnetic field, we observe the appearance of two plasmon-like modes whose corresponding effective plasma frequency grows with the magnetic field and is not supported by any background charge density. Finally, we identify a mode collision which allows us to study the radius of convergence of the linearized hydrodynamics expansion as a function of the external magnetic field. We find that the radius of convergence in momentum space, related to the diffusive transverse electromagnetic mode, increases quadratically with the strength of the magnetic field.