SLE ${}_{8/3}$的多点通过概率和格林函数
Multi-point passage probabilities and Green's functions for SLE${}_{8/3}$
摘要：
我们考虑了$O(n)$模型在临界点处的循环表示。当$n=0$时，模型表示自避免循环的集合（即，它对应于具有$κ=8/3$的SLE），并且可以通过具有中心电荷$c=0$的对数共形场论（LCFT）来描述。我们着重讨论了包含体中扭转算符的上半平面中的关联函数和一对边界单支算符。通过使用库仑气体表示的关联函数，我们得到明确的结果的概率SLE ${}_{8/3}$迹风以各种方式约$N\geq 1$标记点。当点成对崩溃的概率减少到多点格林函数。我们提出了一个显式表示的格林函数的关联函数的散装1/3重量的运营商，和一对边界单腿运营商。
英文摘要：
We consider a loop representation of the $O(n)$ model at the critical point. When $n=0$ the model represents ensembles of self-avoiding loops (i.e., it corresponds to SLE with $κ=8/3$), and can be described by the logarithmic conformal field theory (LCFT) with central charge $c=0$. We focus on the correlation functions in the upper-half plane containing the twist operators in the bulk, and a pair of the boundary one-leg operators. By using a Coulomb gas representation for the correlation functions, we obtain explicit results for probabilities of the SLE${}_{8/3}$ trace to wind in various ways about $N\geq 1$ marked points. When the points collapse pairwise the probabilities reduce to multi-point Green's functions. We propose an explicit representation for the Green's functions in terms of the correlation functions of the bulk 1/3-weight operators, and a pair of the boundary one-leg operators.
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