On the Velocity in the Effective Field Theory of Large Scale Structures
  We compute the renormalized two-point functions of density, divergence and
vorticity of the velocity in the Effective Field Theory of Large Scale
Structures. Because of momentum and mass conservation, the corrections from
short scales to the large-scale power spectra of density, divergence and
vorticity must start at order $k^{4}$. For the vorticity this constitutes one
of the two leading terms. Exact (approximated) self-similarity of an
Einstein-de Sitter ($\Lambda$CDM) background fixes the time dependence so that
the vorticity power spectrum at leading order is determined by the symmetries
of the problem and the power spectrum around the non-linear scale. We show that
to cancel all divergences in the velocity correlators one needs new
counterterms. These fix the definition of velocity and do not represent new
properties of the system. For an Einstein-de Sitter universe, we show that all
three renormalized cross- and auto-correlation functions have the same
structure but different numerical coefficients, which we compute. We elucidate
the differences between using momentum and velocity.
