Lattice calculation of the QGP viscosities - Present results and next project -

The shear and bulk viscosities of gluon plasma are calculated by accumulating a large amount of data for the Matsubara Green function ($G_{\beta}(t_m)$) on isotropic $24^3 \times 8$ and $16^3 \times 8$ lattices. In the case of Iwasaki's improved action, the calculations of $G_{\beta}(t_m)$ are carried out on roughly 6 million configurations, while for the standard action the calculations are done on more than 16 million configurations. The shear viscosities increase roughly with $T^3$, and $\eta/s$ ratios are close to the KSS lower bound in the region where $1<T/T_c<25$. Using these data the bulk viscosities are also determined in the region where $T/T_c < 2$. They are roughly one order of magnitude smaller than the shear viscosities. Our next target is to determine the transport coefficients more precisely by a maximum-entropy method. For this purpose the most effective method may be to adopt an anisotropic lattice. In this report, we study the possible systematic error due to the deformation of the anisotropic lattice at short distances. Near the critical temperature, it is found that the standard action suffers from a large deformation on the anisotropic lattice at short distances, while the deformation is slight for Iwasaki's improved action. To reduce the fluctuation of the Matsubara Green function, the improvement of the energy momentum tensor operator by using clover-type loops is promising. We are also attempting to apply the multi-level algorithm to reduce fluctuation.