The continuum limit of three-dimensional SU(2) lattice Yang–Mills theory on a torus I: Foundations and classical fields
We consider the Wilson lattice gauge measure for $\mathrm{SU}(2)$ on a periodic three-dimensional torus of fixed size, with bare coupling $g^2=g_3^2a$ proportional to the lattice spacing $a$, as dictated by the superrenormalizability of three-dimensional Yang–Mills theory. Observables are Wilson loops of the lattice configuration evolved by the Wilson flow, the lattice gradient flow of the Wilson action, at positive flow time. We prove that, at every fixed value of the coupling, the joint laws of finitely many flowed Wilson loops converge as the lattice spacing tends to zero along the…
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