Transport and hydrodynamics in the chiral limit

Abstract

We analyze the evolution of hydrodynamic fluctuations for QCD matter below $T_c$ in the chiral limit, where the pions (the Goldstone modes) must be treated as additional non-abelian superfluid degrees of freedom, reflecting the broken $S{U}_L(2)\times S{U}_R(2)$ symmetry of the theory. In the presence of a finite pion mass $m_{\pi }$, the hydrodynamic theory is ordinary hydrodynamics at long distances, and superfluid-like at short distances. The presence of the superfluid degrees of freedom then gives specific contributions to the bulk viscosity, the shear viscosity, and diffusion coefficients of the ordinary theory at long distances which we compute. This determines, in some cases, the leading dependence of the transport parameters of QCD on the pion mass. We analyze the predictions of this computation, as the system approaches the $O(4)$ critical point.

arXiv comment27 pages, 2 figures. Correct a mistake, some of the results are slightly modified the conclusion are not changed .Corrected typos. Added references

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• The causality and stability of relativistic spin-hydrodynamics
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• Soft modes in hot QCD matter
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