Extracting continuum properties of quantum field theories from discretized
spacetime is challenging due to lattice artifacts. Renormalization-group
(RG)-improved lattice actions can preserve continuum properties, but are in
general difficult to parameterize. Machine learning (ML) with gauge-equivariant
convolutional neural networks provides a way to efficiently describe such
actions. We test a machine-learned RG-improved lattice gauge action, the
classically perfect fixed-point (FP) action, for four-dimensional SU(3) gauge
theory through Monte Carlo simulations. We establish that the gradient flow of
the FP action is free of tree-level discretization effects to all orders in the
lattice spacing, making it classically perfect. This allows us to test the
quality of improvement of the FP action, without introducing additional
artifacts. We find that discretization effects in gradient-flow observables are
highly suppressed and less than 1% up to lattice spacings of 0.14 fm, allowing
continuum physics to be extracted from coarse lattices. The quality of
improvement achieved motivates the use of the FP action in future gauge theory
studies. The advantages of ML-based parameterizations also highlight the
possibility of realizing quantum perfect actions in lattice gauge theory.

Cet article explore les excursions dans le temps et leurs implications.

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