  Within the framework of holography, the Einstein-Maxwell action with
Dirichlet boundary conditions corresponds to a dual conformal field theory in
presence of an external gauge field. Nevertheless, in many real-world
applications, e.g., magnetohydrodynamics, plasma physics, superconductors, etc.
dynamical gauge fields and Coulomb interactions are fundamental. In this work,
we consider bottom-up holographic models at finite magnetic field and (free)
charge density in presence of dynamical boundary gauge fields which are
introduced using mixed boundary conditions. We numerically study the spectrum
of the lowest quasi-normal modes and successfully compare the obtained results
to magnetohydrodynamics theory in $2+1$ dimensions. Surprisingly, as far as the
electromagnetic coupling is small enough, we find perfect agreement even in the
large magnetic field limit. Our results prove that a holographic description of
magnetohydrodynamics does not necessarily need higher-form bulk fields but can
be consistently derived using mixed boundary conditions for standard gauge
fields.
