平面UST分支与$c=-2$退化边界关联
Planar UST Branches and $c=-2$ Degenerate Boundary Correlations
AI总结：
本文用中心荷$c=-2$的边界共形场论描述有线均匀生成树的分支连接概率，证明其收敛到行列式形式的共形块，并验证BPZ方程及Temperley-Lieb代数作用。
摘要：
我们提供了有线均匀生成树（UST）中边界效应的概率模型的共形场论（CFT）描述及其代数内容，涉及中心荷$c=-2$的Kac表整个第一行。具体而言，我们证明了有线UST中（可能融合的）分支的所有边界到边界连接概率在标度极限下收敛到显式的CFT量，这些量以行列式表示，也可视为中心荷$c=-2$的边界CFT中退化初级场的共形块。此外，我们验证了任意阶的Belavin-Polyakov-Zamolodchikov（BPZ）偏微分方程（即Virasoro退化条件）成立，并揭示了该模型中初级场边界关联函数空间上存在一个潜在的带价Temperley-Lieb代数作用。为证明这些结果，我们将概率技术与表示论相结合。
英文摘要：
We provide a conformal field theory (CFT) description of the probabilistic model of boundary effects in the wired uniform spanning tree (UST) and its algebraic content, concerning the entire first row of the Kac table with central charge $c=-2$. Namely, we prove that all boundary-to-boundary connection probabilities for (potentially fused) branches in the wired UST converge in the scaling limit to explicit CFT quantities, expressed in terms of determinants, which can also be viewed as conformal blocks of degenerate primary fields in a boundary CFT with central charge $c=-2$. Moreover, we verify that the Belavin-Polyakov-Zamolodchikov (BPZ) PDEs (i.e., Virasoro degeneracies) of arbitrary orders hold, and we also reveal an underlying valenced Temperley-Lieb algebra action on the space of boundary correlation functions of primary fields in this model. To prove these results, we combine probabilistic techniques with representation theory.
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。
