To obtain the precise values of the bulk quantities and transport coefficients in quark-gluon-plasma phase, we propose that a direct calculation of the renormalized energy-momentum tensor (EMT) on the lattice using the gradient flow.
From one-point function of EMT, authors in Ref. obtained the interaction measure and thermal entropy. The results are consistent with the one obtained by the integral method.
Based on the success, we try to measure the two-point function of EMT, which is related to the transport coefficients.
Advantages of our method are (1) a clear signal because of the smearing effects of the gradient flow and (2) no need to calculate the wave function renormalization of EMT.
In addition, we give a short remark on a comparison of the numerical cost between the positive- and adjoint-flow methods for fermions, needed to obtain the EMT in the (2+1) flavor QCD.