TNT Colloquium Hydrodynamic fluctuations and chiral corrections to transport coefficient[Duke]

First, I review hydrodynamic fluctuations and why they
are important to the search for the QCD critical point. I discuss
how stochastic hydrodynamics leads (though loops) to long
time tails which appear to the 1.5 order in the gradient expansion.
Subsequently, I use this knowledge to discuss hydrodynamics in approximately
the chiral limit (below the critical temperate), where the appropriate effective theory is a non-abelian generalization
of superfluid hydrodynamics. This hydrodynamic theory is corrected
by the pion mass, and therefore approaches ordinary hydrodynamics in the very long wavelength
limit. Integrating out the superfluid modes, in analogy to the long time tails, yields the
first correction from a finite quark mass to the bulk viscosity of QCD. This correction
is proportional to the 0.5 order in the quark mass .