Neural network interpolators for Wilson loops

TL;DR

This paper introduces a neural network-based approach to improve the extraction of static quark-antiquark potentials from lattice QCD by constructing gauge-equivariant trial states for better state identification.

Contribution

It presents a novel neural-network parametrization of trial states with gauge-equivariant layers, enabling automatic interpolation of ground and excited states in quenched lattice QCD.

Findings

Successfully obtains interpolators for ground and excited states.

Improves state extraction without complex shape trial states.

Uses neural networks with gauge-equivariant layers for better results.

Abstract

The extraction of the static quark-antiquark potential from lattice QCD suffers from the poor signal-to-noise ratio of Wilson loops at large Euclidean times. To overcome this, smearing methods or the Coulomb gauge are used to improve the ground-state overlap with respect to the straight Wilson line trial state within the Wilson loop. To find excited states, complicated shapes are introduced to generate specific quantum numbers. Here, we introduce a neural-network parametrization of trial states, constructed with gauge-equivariant layers and optimized with a loss function that favors ground and excited states. In the quenched theory, we automatically obtain the interpolators for the ground and excited states.