  We construct a Schwinger-Keldysh effective field theory for relativistic
hydrodynamics for charged matter in a thermal background using a superspace
formalism. Superspace allows us to efficiently impose the symmetries of the
problem and to obtain a simple expression for the effective action. We show
that the theory we obtain is compatible with the Kubo-Martin-Schwinger
condition, which in turn implies that Green's functions obey the
fluctuation-dissipation theorem. Our approach complements and extends existing
formulations found in the literature.
