  We present a detailed and self-contained analysis of the universal
Schwinger-Keldysh effective field theory which describes macroscopic thermal
fluctuations of a relativistic field theory, elaborating on our earlier
construction in arXiv:1511.07809. We write an effective action for appropriate
hydrodynamic Goldstone modes and fluctuation fields, and discuss the symmetries
to be imposed. The constraints imposed by fluctuation-dissipation theorem are
manifest in our formalism. Consequently, the action reproduces hydrodynamic
constitutive relations consistent with the local second law at all orders in
the derivative expansion, and captures the essential elements of the eightfold
classification of hydrodynamic transport of arXiv:1502.00636. We demonstrate
how to recover the hydrodynamic entropy and give predictions for the
non-Gaussian hydrodynamic fluctuations.
  The basic ingredients of our construction involve (i) doubling of degrees of
freedom a la Schwinger-Keldysh, (ii) an emergent thermal gauge symmetry
associated with entropy which is encapsulated in a Noether current a la Wald,
and (iii) a BRST/topological supersymmetry imposing the fluctuation-dissipation
theorem a la Parisi-Sourlas. The overarching mathematical framework for our
construction is provided by the balanced equivariant cohomology of thermal
translations, which captures the basic constraints arising from the
Schwinger-Keldysh doubling, and the thermal Kubo-Martin-Schwinger relations.
All these features are conveniently implemented in a covariant superspace
formalism. An added benefit is that the second law can be understood as being
due to entropy inflow from the Grassmann-odd directions of superspace.
