Twist operator correlation functions in O ( n ) loop models
Twist operator correlation functions in O ( n ) loop models
复制标题
O(n)循环模型中的扭曲算子相关函数
DOI：
10.1088/1751-8113/42/23/235001
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Simmons J
中科院分区：
文献类型：
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作者：
Simmons J
利用共形场论方法计算了O (n)模型在临界点处的环表示中几何观测值的相关函数。我们关注包含扭转算子的相关函数，将它们与锚定环、SLE过程边界和双SLE过程相结合。我们进一步关注n= 0，表示自回避环，它对应于c= 0的对数共形场理论（LCFT）。在这个极限中，扭转算子扮演了0权重指示算子的角色，我们通过与已知示例的比较验证了这一点。利用扭曲算子零态施加的附加条件，我们得到了一个新的明确结果，即SLE 8/3以各种方式绕上半平面上两点旋转的概率，例如SLE通过这两个点的左侧。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，突出了由理论中应力张量的两个不同对数伙伴的存在引起的潜在不兼容性。我们认为这两个伙伴确实出现在理论中，一个在体中，一个在边界上，并且不相容是由限制性体-边界融合规则解决的。
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 0-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 winds in various ways about two points in the upper half-plane, eg 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 argue 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.