We use the framework of generalised global symmetries to study various
hydrodynamic regimes of hot electromagnetism. We formulate the hydrodynamic
theories with an unbroken or a spontaneously broken U(1) one-form symmetry. The
latter of these describes a one-form superfluid, which is characterised by a
vector Goldstone mode and a two-form superfluid velocity. Two special limits of
this theory have been studied in detail: the string fluid limit where the U(1)
one-form symmetry is partly restored, and the electric limit in which the
symmetry is completely broken. The transport properties of these theories are
investigated in depth by studying the constraints arising from the second law
of thermodynamics and Onsager's relations at first order in derivatives. We
also construct a hydrostatic effective action for the Goldstone modes in these
theories and use it to characterise the space of all equilibrium
configurations. To make explicit contact with hot electromagnetism, the
traditional treatment of magnetohydrodynamics, where the electromagnetic photon
is incorporated as dynamical degrees of freedom, is extended to include
parity-violating contributions. We argue that the chemical potential and
electric fields are not independently dynamical in magnetohydrodynamics, and
illustrate how to eliminate these within the hydrodynamic derivative expansion
using Maxwell's equations. Additionally, a new hydrodynamic theory of
non-conducting, but polarised, plasmas is formulated, focusing primarily on the
magnetically dominated sector. Finally, it is shown that the different limits
of one-form superfluids formulated in terms of generalised global symmetries
are exactly equivalent to magnetohydrodynamics and the hydrodynamics of
non-conducting plasmas at the non-linear level.Comment: v3: 69 + 1 pages, 1 figure, added clarifications and appendix with
discrete symmetries, to be published in JHE