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We study correlation functions of the energy-momentum tensor (EMT) in$(2+1)$-flavor full QCD to evaluate QGP viscosities. We adopt nonperturbativelyimproved Wilson fermion and Iwasaki gauge action. Our degenerate $u$, $d$ quarkmass is rather heavy with $m_{\pi}/m_{\rho}\simeq0.63$, while the $s$ quarkmass is set to approximately its physical value. Performing simulations onlattices with $N_t=16$ to 6 at a fine lattice spacing of $a=0.07$ fm, thetemperature range of $T\simeq174$--$464$ MeV is covered using the fixed-scaleapproach. We attempt to compute viscosities by three steps: (1) calculate twopoint correlation functions of non-perturbatively renormalized EMT applying thegradient flow method, (2) derive the spectral function from correlationfunction, and (3) extract viscosities from the spectral function applying theKubo formula. We report on the status of the project and present preliminaryresults for the shear viscosity in the high temperature phase.

Study of energy-momentum tensor correlation function in $N_f=2+1$ full QCD for QGP viscosities