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PreprintCC0arXiv

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 the rescaled logarithmic field converges to the solution of the one-form stochastic heat equation in probability. In particular, the limiting dynamics are universal and do not depend on the higher-order details of the plaquette action.

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Cite

BibTeXRIS
BibTeX
@misc{chevyrev2026scaling,
  title = {{Scaling limit of the 3D abelian Yang--Mills Langevin dynamics}},
  author = {Ilya Chevyrev and Yahui Qu and Hao Shen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.27828},
  eprint = {2608.27828},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.27828},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Scaling limit of the 3D abelian Yang--Mills Langevin dynamics
AU  - Ilya Chevyrev
AU  - Yahui Qu
AU  - Hao Shen
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2608.27828
UR  - https://arxiv.org/abs/2608.27828
AB  - 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 the rescaled logarithmic field converges to the solution of the one-form stochastic heat equation in probability. In particular, the limiting dynamics are universal and do not depend on the higher-order details of the plaquette action.
ER  -