微分系统的回路方程
Loop equations from differential systems
摘要：
对于任何微分系统$dΨ=ΦΨ$，其中$Ψ$属于李群（主丛的纤维），$Φ$是黎曼曲面$Σ$上的李代数$\mathfrak g$值为1的形式，与一个无限序列的“交换子”$W_n$相关联，这些交换子是$Σ^n$上的对称$n$ -形式。本文的目的是证明这些迭代器总是满足“循环方程”，即随机矩阵模型中的关联函数所满足的相同方程，或CFT中的Virasoro或W-代数约束所满足的相同方程。
英文摘要：
To any differential system $dΨ=ΦΨ$ where $Ψ$ belongs to a Lie group (a fiber of a principal bundle) and $Φ$ is a Lie algebra $\mathfrak g$ valued 1-form on a Riemann surface $Σ$, is associated an infinite sequence of "correlators" $W_n$ that are symmetric $n$-forms on $Σ^n$. The goal of this article is to prove that these correlators always satisfy "loop equations", the same equations satisfied by correlation functions in random matrix models, or the same equations as Virasoro or W-algebra constraints in CFT.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
