  We discuss the physics of momentum diffusion in a charged plasma. Following
the holographic strategy outlined in arXiv:2012.03999 we construct an open
effective field theory for the low-lying modes of the conserved currents. The
charged plasma is modeled holographically in terms of a Reissner-Nordstrom-AdS
black hole. We analyze graviton and photon fluctuations about this background,
decoupling in the process the long-lived momentum diffusion mode from the
short-lived charged transport mode. Furthermore, as in the aforementioned
reference, we argue that the dynamics of these modes are captured by a set of
designer scalars in the background geometry. These scalars have their
gravitational coupling modulated by an auxiliary dilaton with long-lived modes
being weakly coupled near the spacetime asymptopia. Aided by these
observations, we obtain the quadratic effective action that governs the
fluctuating hydrodynamics of charge current and stress tensor, reproducing in
the process transport data computed previously. We also point out an
interesting length scale lying between the inner and outer horizon radii of the
charged black hole associated with Ohmic conductivity.
