论文标题
对数CFT的通用中心收费：从Liouville理论到$ Q $ - 州Potts模型
Logarithmic CFT at generic central charge: from Liouville theory to the $Q$-state Potts model
论文作者
论文摘要
使用基本田地的衍生物（无效）相对于保形维度，我们在通用中央电荷中建立了保形代数的非平凡对数表示的无限家族，约旦的尺寸为$ 2 $或$ 3 $。每个表示都带有一个自由参数，该参数在对退化字段的存在的假设下采用固定值。该参数可以看作是对数耦合的更简单，非归一化的重新定义。在中央电荷零的真空模块的示例中，此参数表征了尺寸$ 3 $的Jordan块，并取值$ - \ frac {1} {48} $。 我们计算相应的非手续保形块，尽管它们通常不满足任何非平凡的微分方程。我们表明，这些块出现在liouville理论的范围内四点函数。 作为一个应用程序，我们描述了关键的二维$ o（n）$和$ q $ $ $ - 状态potts模型的对数结构。我们描述的有效性通过$ q $ - 州Potts模型中的半分析自动启动四点连接到任意精度。此外，我们为Delfino-Viti猜想提供了三点连接性的数值证据。我们的结果适用于复杂平面及其他地区的$ Q $的通用值。
Using derivatives of primary fields (null or not) with respect to the conformal dimension, we build infinite families of non-trivial logarithmic representations of the conformal algebra at generic central charge, with Jordan blocks of dimension $2$ or $3$. Each representation comes with one free parameter, which takes fixed values under assumptions on the existence of degenerate fields. This parameter can be viewed as a simpler, normalization-independent redefinition of the logarithmic coupling. In the example of the vacuum module at central charge zero, this parameter characterizes a Jordan block of dimension $3$, and takes the value $-\frac{1}{48}$. We compute the corresponding non-chiral conformal blocks, although they in general do not satisfy any nontrivial differential equation. We show that these blocks appear in limits of Liouville theory four-point functions. As an application, we describe the logarithmic structures of the critical two-dimensional $O(n)$ and $Q$-state Potts models at generic central charge. The validity of our description is demonstrated by semi-analytically bootstrapping four-point connectivities in the $Q$-state Potts model to arbitrary precision. Moreover, we provide numerical evidence for the Delfino--Viti conjecture for the three-point connectivity. Our results hold for generic values of $Q$ in the complex plane and beyond.
