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We investigate a trajectory for the Wilson flow in the theory space. For thispurpose, we determine the coefficient of the plaquette and rectangular terms inthe action for the configurations defined by the solution of the Wilson flow.The demon method regarded as one of the inverse Monte Carlo methods is used forthe determination of them. Starting from the conventional Wilson plaquetteaction of quenched QCD, we find that the coefficient of the plaquette growswhile that of the rectangular tends to negative with the development of theflow as the known improved actions. We also find that the trajectory forms astraight line in the two-coupling theory space.

Effective lattice action for the configurations smeared by the Wilson flow