Effective lattice action for the configurations smeared by the Wilson flow

TL;DR

This paper explores the evolution of lattice gauge configurations under Wilson flow, determining an effective action with specific coefficients that describe the flow trajectory in theory space.

Contribution

It introduces a method to derive an effective lattice action along the Wilson flow trajectory using the demon method, revealing a linear trajectory in coupling space.

Findings

The plaquette coefficient increases with flow time.

The rectangular term coefficient becomes negative as flow develops.

The flow trajectory is approximately a straight line in coupling space.

Abstract

We investigate a trajectory for the Wilson flow in the theory space. For this purpose, we determine the coefficient of the plaquette and rectangular terms in the 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 for the determination of them. Starting from the conventional Wilson plaquette action of quenched QCD, we find that the coefficient of the plaquette grows while that of the rectangular tends to negative with the development of the flow as the known improved actions. We also find that the trajectory forms a straight line in the two-coupling theory space.