$\mathrm{SU(N)}$ lattice gauge theories with Physics-Informed Neural Networks

TL;DR

This paper introduces a Physics-Informed Neural Network approach to study $ ext{SU}(N)$ lattice gauge theories, enabling the computation of eigenstates across different coupling regimes without supervision.

Contribution

The authors develop a PINN-based method that encodes gauge theory equations and symmetries, allowing unsupervised spectral analysis of lattice gauge theories.

Findings

Successfully reproduces energy spectra of $ ext{U}(1)$ and $ ext{SU}(2)$ gauge theories

Enables smooth transition from strong to weak coupling regimes

Validates the approach on single-plaquette models

Abstract

We present an application of Physics-Informed Neural Networks (PINNs) to the study of $\mathrm{SU}(N_c)$ lattice gauge theories. Our method enables the learning of eigenfunctions and eigenvalues at arbitrary gauge couplings, smoothly moving from the analytically known strong-coupling regime towards weaker couplings. By encoding the Schr\"odinger equation and the symmetries of the eigenstates directly into the loss function, the network performs an unsupervised exploration of the spectrum. We validate the approach on the single-plaquette $\mathrm{U}(1)$ and $\mathrm{SU}(2)$ pure-gauge theories, showing that the PINNs successfully reproduce the hierarchy of energy levels and their corresponding wavefunctions.