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

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Nakamura, Sunao Sakai Atsushi

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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.

Comment: 8 pages, 5 figures, The XXV International Symposium on Lattice Field Theory(Regensburg, 2007)

Comment: 8 pages, 5 figures, The XXV International Symposium on Lattice Field Theory(Regensburg, 2007)

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High Energy Physics - Lattice