# 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 .