SU(N) lattice gauge theories with Physics-Informed Neural Networks

2025/10/30 by Romiti, Simone
#FOS: Physical sciences #High Energy Physics - Lattice (hep-lat)

paper · doi:10.48550/arxiv.2510.26904

Abstract

We present an application of Physics-Informed Neural Networks (PINNs) to the study of 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 Schrödinger 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 U(1) and SU(2) pure-gauge theories, showing that the PINNs successfully reproduce the hierarchy of energy levels and their corresponding wavefunctions.

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