Sampling from the Boltzmann distributions of lattice gauge theories — the computational backbone of first-principles QCD and related models — grows increasingly difficult as the gauge coupling weakens. Traditional Monte Carlo methods suffer from critical slowing down and topological freezing, and recent machine-learning approaches built in link space face their own obstacle: correlations in that representation become long-ranged precisely in the weak-coupling regime relevant to continuum physics. This unreviewed preprint, posted to arXiv and not yet peer-reviewed, proposes a different starting point.
The authors argue that plaquette variables are the more natural home for generative modeling because the action is local in those variables. The catch is that plaquettes are not independent: they satisfy Bianchi constraints that confine them to a lower-dimensional manifold. To handle this exactly, the paper introduces a multilevel normalizing-flow architecture — a coarse-to-fine factorization in which each refinement step reduces the global constraint problem to a sequence of local solves. Crucially, the size of each local constraint problem does not grow with the lattice, keeping the construction scalable.
The authors validate their Plaquette-Space Sampler (PSS) for U(1) gauge theory in two and four dimensions and for SU(2) in two dimensions, reporting substantial improvements in sampling quality over link-space baselines. The performance gap widens toward weak coupling, which the paper identifies as the regime of greatest practical importance for asymptotically free theories. The claims are promising, but independent peer review has not yet assessed the methodology or the scope of the benchmark comparisons.