Viscosities of Hot Gluon -- A Lattice QCD Study --
  We present transport coefficients (shear viscosity, $\eta$, and bulk viscosity, $\zeta$) for the gluon system obtained by the lattice QCD. This is an indispensable calculation towards the understanding of ``New State of Matter'' observed in RHIC. We study the temperature regions of RHIC ($1.4 \leq T/T_c \leq 1.8$) and much higher ones up to $ T/T_c \sim 20$. In RHIC regions, the ratio of shear viscosity to entropy density, $\eta/s$, is around $\sim 0.1-0.4$, and satisfies the KSS bound. At high temperature, $\eta$ becomes two or three oder of magnitude larger. Our calculation has two limitations: (i) the use of the quench approximation, i.e., without quark pair creation-annihilation effects on vacuum, and (ii) the use of an ansatz for the spectral function. The first point has been well studied in calculations of the spectroscopy and the phase-transition behavior. To investigate the second point, we compare our results with perturbative calculations in high $T$-regions, and also check the effects of the modification of the spectral function on the viscosity. 
A. Nakamura and S. Sakai