标题： 多个SLEs对于$κ\in (0,8)$：库仑气体积分和纯划分函数 显示英文标题

标题： Multiple SLEs for $κ\in (0,8)$: Coulomb gas integrals and pure partition functions

摘要： 在本文中，我们给出了SLE分割函数与共形场论的库仑气体形式之间的显式关系。 我们首先构造了一族SLE${}_\kappa$分割函数作为库仑气体积分，并推导了它们的各种性质。 根据环$O(n)$模型中的概率相关性的解释，当$\kappa\in (8/3,8)$时，它们总是正的，而当$\kappa\leq 8/3$时，它们可能有零点。 它们还具有一个弗罗贝尼乌斯级数展开，这与CFT中的代数内容相匹配。 此外，我们检查到在融合的第一层，当$\kappa=8/3$和$\kappa=8$时，它们具有对数渐近行为，这与对数最小模型$M(2,1)$和$M(2,3)$分别一致。 其次，我们构建SLE${}_\kappa$纯分割函数并证明它们在$\kappa\in (0,8)$上是连续的，并且当$(8-\kappa)$增大时以$\kappa\to 8$的多项式形式衰减到零。 我们明确地通过路径矩阵将库仑气体积分和纯分割函数联系在一起。 作为副产品，我们的结果给出了全局非简单多重弦状SLE${}_\kappa$测度（$\kappa \in (4,8)$）的构造，该测度由其重新采样性质唯一确定。 显示英文摘要

摘要： In this article, we give an explicit relationship of SLE partition functions with Coulomb gas formalism of conformal field theory. We first construct a family of SLE${}_\kappa$ partition functions as Coulomb gas integrals and derive their various properties. In accordance with an interpretation as probabilistic correlations in loop $O(n)$ models, they are always positive when $\kappa\in (8/3,8)$, while they may have zeroes for $\kappa\leq 8/3$. They also admit a Fr\"{o}benius series expansion that matches with the algebraic content from CFT. Moreover, we check that at the first level of fusion, they have logarithmic asymptotic behavior when $\kappa=8/3$ and $\kappa=8$, in accordance with logarithmic minimal models $M(2,1)$ and $M(2,3)$, respectively. Second, we construct SLE${}_\kappa$ pure partition functions and show that they are continuous in $\kappa\in (0,8)$ and they decay to zero as a polynomial of $(8-\kappa)$ when $\kappa\to 8$. We explicitly relate the Coulomb gas integrals and pure partition functions together in terms of the meander matrix. As a by-product, our results yield a construction of global non-simple multiple chordal SLE${}_\kappa$ measures ($\kappa \in (4,8)$) uniquely determined by their re-sampling property.