Exploring gauge-fixing conditions with gradient-based optimization

TL;DR

This paper introduces a differentiable parameterization of gauge fixing in lattice gauge theories, enabling gradient-based optimization to explore and select gauge schemes that optimize specific target functions, enhancing computational efficiency.

Contribution

It presents a novel differentiable framework for gauge fixing that encompasses multiple gauges and uses the adjoint state method for optimization.

Findings

Enables systematic exploration of gauge-fixing schemes.

Allows optimization of gauge conditions for specific targets.

Supports various gauge choices like Landau, Coulomb, and maximal tree gauges.

Abstract

Lattice gauge fixing is required to compute gauge-variant quantities, for example those used in RI-MOM renormalization schemes or as objects of comparison for model calculations. Recently, gauge-variant quantities have also been found to be more amenable to signal-to-noise optimization using contour deformations. These applications motivate systematic parameterization and exploration of gauge-fixing schemes. This work introduces a differentiable parameterization of gauge fixing which is broad enough to cover Landau gauge, Coulomb gauge, and maximal tree gauges. The adjoint state method allows gradient-based optimization to select gauge-fixing schemes that minimize an arbitrary target loss function.