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Machine-Learned Renormalization-Group-Improved Gauge Actions and Classically Perfect Gradient Flows.

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Machine learning efficiently describes lattice gauge actions, enabling extraction of continuum properties from quantum field theories. A machine-learned action significantly reduces discretization errors, allowing precise physics extraction from coarse lattices.

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Area of Science:

  • High Energy Physics
  • Computational Physics
  • Quantum Field Theory

Background:

  • Extracting continuum properties from discretized spacetime in quantum field theories is hindered by lattice artifacts.
  • Renormalization-group (RG)-improved lattice actions can preserve continuum properties but are challenging to parameterize.
  • Machine learning (ML) offers an efficient method for describing complex lattice actions.

Purpose of the Study:

  • To test a machine-learned RG-improved lattice gauge action, specifically the classically perfect fixed-point (FP) action.
  • To evaluate the effectiveness of the FP action in mitigating discretization effects in four-dimensional SU(3) gauge theory.
  • To demonstrate the potential of ML in developing improved lattice actions for quantum field theory.

Main Methods:

  • Utilized Monte Carlo simulations to test the classically perfect fixed-point (FP) action for SU(3) gauge theory.
  • Employed gauge-equivariant convolutional neural networks for ML-based parameterization of the RG-improved action.
  • Analyzed gradient flow observables to quantify discretization effects.

Main Results:

  • The gradient flow of the FP action is confirmed to be free of tree-level discretization effects to all orders in lattice spacing.
  • Discretization effects in gradient-flow observables are suppressed to less than 1% even for lattice spacings up to 0.14 fm.
  • The FP action demonstrates significant improvement, enabling continuum physics extraction from coarse lattices.

Conclusions:

  • The machine-learned FP action is highly effective in suppressing discretization artifacts, facilitating continuum physics extraction.
  • The quality of improvement achieved validates the use of the FP action in future lattice gauge theory studies.
  • ML-based parameterizations show promise for realizing quantum perfect actions in lattice gauge theory.