The gradient flow bears a close resemblance to the coarse graining, the guiding principle of the renormalization group (RG). In the case of scalar field theory, a precise connection has been made between the gradient flow and the RG flow of the Wilson action in the exact renormalization group (ERG) formalism. By imitating the structure of this connection, we propose an ERG differential equation that preserves manifest gauge invariance in Yang–Mills theory. Our construction in continuum theory can be extended to lattice gauge theory.

中文翻译：

---

梯度流精确重整化组

梯度流与重整化群 (RG) 的指导原则——粗粒度非常相似。在标量场论的情况下，梯度流和威尔逊作用的 RG 流在精确重整化群 (ERG) 形式中建立了精确的联系。通过模仿这种连接的结构，我们提出了一个 ERG 微分方程，它保留了 Yang-Mills 理论中明显的规范不变性。我们在连续统理论中的构造可以扩展到格规范理论。