O（n）圈模型中的扭算子关联函数
Twist operator correlation functions in O(n) loop models
摘要：
利用共形场论方法，我们计算了O（n）模型在临界点的圈表示中几何观测量的关联函数。我们专注于关联函数包含扭曲运营商，结合这些与锚定循环，边界与SLE过程和双SLE过程。我们进一步集中在n=0，表示自避免回路，这对应于对数共形场论（LCFT）与c=0。在这个限制的扭曲运营商起着零权重指标运营商，我们验证与已知的例子进行比较的作用。利用扭曲算子零态所施加的附加条件，我们得到了一个新的显式结果的概率，SLE_{8/3}风以各种方式在上半平面的两个点，例如，SLE通过这两个点的左边。我们用来推导缠绕概率的c=0对数CFT算子的集合是新颖的，突出了理论中存在两个不同的对数伙伴对应力张量造成的潜在不相容性。我们提供的证据表明，这两个合作伙伴确实出现在理论中，一个在批量和一个在边界上，并解决限制性批量边界融合规则的不兼容性。
英文摘要：
Using conformal field theoretic methods we calculate correlation functions of geometric observables in the loop representation of the O(n) model at the critical point. We focus on correlation functions containing twist operators, combining these with anchored loops, boundaries with SLE processes and with double SLE processes. We focus further upon n=0, representing self-avoiding loops, which corresponds to a logarithmic conformal field theory (LCFT) with c=0. In this limit the twist operator plays the role of a zero weight indicator operator, which we verify by comparison with known examples. Using the additional conditions imposed by the twist operator null-states, we derive a new explicit result for the probabilities that an SLE_{8/3} wind in various ways about two points in the upper half plane, e.g. that the SLE passes to the left of both points. The collection of c=0 logarithmic CFT operators that we use deriving the winding probabilities is novel, highlighting a potential incompatibility caused by the presence of two distinct logarithmic partners to the stress tensor within the theory. We provide evidence that both partners do appear in the theory, one in the bulk and one on the boundary and that the incompatibility is resolved by restrictive bulk-boundary fusion rules.
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