English

A para-controlled approach to the stochastic Yang-Mills equation in two dimensions

Probability 2025-08-15 v2 Mathematical Physics Analysis of PDEs math.MP

Abstract

We consider the stochastic Yang-Mills heat equation on the two-dimensional torus. Using regularity structures, Chandra, Chevyrev, Hairer, and Shen previously proved both the local well-posedness and gauge-covariance of this model. In this article, we revisit their results using para-controlled calculus. One of the main ingredients is a new coordinate-invariant perspective on vector-valued stochastic objects.

Keywords

Cite

@article{arxiv.2305.07197,
  title  = {A para-controlled approach to the stochastic Yang-Mills equation in two dimensions},
  author = {Bjoern Bringmann and Sky Cao},
  journal= {arXiv preprint arXiv:2305.07197},
  year   = {2025}
}

Comments

89 pages. Minor revisions. To appear in Mem. Amer. Math. Soc