Study of Dynamical Properties around the QCD Critical Points based on Chiral Effective Theory

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We have shown on the basis of the chiral effective theory that the QCD matter can have a multiple-critical points structure under charge neutrality. The soft dynamics around the typical QCD critical point has been shown to be dominated by the energy fluctuations. A generic class of hydrodynamic equations for a viscous fluid has been derived by applying the so called renormalization-group method. We have shown that the mysterious early thermalization of the QCD matter suggested by RHIC experiments can be attributed to the chaotic behavior of the nonlinear dynamics of the classical Yang-Mills field. A novel diagrammatical method for computing the transport coefficients in the relativistic quantum field theory has been developed. We have established that the quark spectral function gets to develop an ultrasoft mode at high temperature generically.