AI 中文总结
该研究证明了紧致曲面上二维规范理论的普适性定理，将随机过程不变性原理拓展至规范理论领域，涵盖多种格点规范理论及Yang-Mills和乐过程，通过状态和公式完成证明。
AI 中文摘要
我们证明了紧致曲面上一大类二维规范理论的普适性定理。紧致连通李群上每个可容许的共轭不变Lévy过程，都确定了一类格点规范理论的普适类，其连续极限为对应的马尔可夫和乐过程。该结果可视为随机游走与Lévy过程不变性原理的规范理论类比，框架包含Yang-Mills和乐过程及标准热核（Villain）、Wilson、Manton格点作用量。证明采用具有独立意义的状态和公式，将依赖于作用量的谱系数与由曲面及环路构型的标记带型决定的不依赖于作用量的拓扑系数分离开来。
英文摘要
We prove a universality theorem for a broad class of two-dimensional gauge theories on compact surfaces. Each admissible conjugation-invariant Lévy process on a compact connected Lie group determines a universality class of lattice gauge theories whose continuum limit is the associated Markovian holonomy process. Our result can be seen as a gauge-theoretic analogue of invariance principles for random walks and Lévy processes. This framework includes the Yang--Mills holonomy process and the standard heat-kernel (Villain), Wilson, and Manton lattice actions. The proof uses state-sum formulas of independent interest, separating action-dependent spectral coefficients from action-independent topological coefficients determined by the surface and the marked ribbon type of the loop configuration.
Comments34 pages, 5 figures. Comments welcome!
