Scaling limit of the 3D abelian Yang--Mills Langevin dynamics

Ilya Chevyrev; Yahui Qu; Hao Shen

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arXiv · 2608.27828

Scaling limit of the 3D abelian Yang--Mills Langevin dynamics

Ilya Chevyrev·Yahui Qu·Hao Shen

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Abstract

We study the continuum scaling limit of the Langevin dynamics for three-dimensional U(1) lattice Yang--Mills theory. The model is defined on the discrete 3D torus with a general class of plaquette actions that are suitably normalized, including Wilson, Manton, and Villain actions. Under the weak-coupling scaling and in the DeTurck gauge, we prove that, locally in time and in probability, the rescaled logarithmic field converges to the solution of the one-form stochastic heat equation. In particular, the limiting dynamics are universal and do not depend on the higher-order details of the plaquette action.

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BibTeX RIS

Ilya Chevyrev, Yahui Qu, Hao Shen. 2026-08-28. Scaling limit of the 3D abelian Yang--Mills Langevin dynamics. https://arxiv.org/abs/2608.27828

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