Quasi-normal modes of dyonic black holes and magneto-hydrodynamics

We revisit the magneto-hydrodynamics in (2+1) dimensions and confirm that it is consistent with the quasi-normal modes of the (3+1) dimensional dyonic black holes in the most general set-up with finite density, magnetic field and wave vector. We investigate all possible modes (sound, shear, diffusion, cyclotron etc.) and their interplay. For the magneto-hydrodynamics we perform a complete and detailed analysis correcting some prefactors in the literature, which is important for the comparison with quasi-normal modes. For the quasi-normal mode computations in holography we identify the independent fluctuation variables of the dyonic black holes, which is nontrivial at finite density and magnetic field. As an application of the quasi-normal modes of the dyonic black holes we investigate a transport property, the diffusion constant. We find that the diffusion constant at finite density and magnetic field saturates the lower bound at low temperature. We show that this bound can be understood from the pole-skipping point.