Gauge-Equivariant Graph Neural Networks for Lattice Gauge Theories

• URL: http://arxiv.org/abs/2604.20797v1
• Date: Wed, 22 Apr 2026 17:21:20 GMT
• Title: Gauge-Equivariant Graph Neural Networks for Lattice Gauge Theories
• Abstract summary: We introduce a gauge-equivariant graph neural network that embeds non-Abelian symmetry directly into message passing via matrix-valued, gauge-covariant features and symmetry-compatible updates.<n>We validate the approach across pure gauge, gauge-matter, and dynamical regimes, establishing gauge-equivariant message passing as a general paradigm for learning in systems governed by local symmetry.
• Score: 1.1928873764689458
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Local gauge symmetry underlies fundamental interactions and strongly correlated quantum matter, yet existing machine-learning approaches lack a general, principled framework for learning under site-dependent symmetries, particularly for intrinsically nonlocal observables. Here we introduce a gauge-equivariant graph neural network that embeds non-Abelian symmetry directly into message passing via matrix-valued, gauge-covariant features and symmetry-compatible updates, extending equivariant learning from global to fully local symmetries. In this formulation, message passing implements gauge-covariant transport across the lattice, allowing nonlocal correlations and loop-like structures to emerge naturally from local operations. We validate the approach across pure gauge, gauge-matter, and dynamical regimes, establishing gauge-equivariant message passing as a general paradigm for learning in systems governed by local symmetry.

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