论文标题
WZW模型中的边界相关器$ _2 $
Boundary correlators in WZW model on AdS$_2$
论文作者
论文摘要
在ADS $ _2 $上定义的一些2D共形场理论中的基本字段的边界相关器具有特别简单的结构。例如，liouville标量的相关器恰好与限于实际线的平面上压力张量的手性分量的相关器相同。在这里，我们在WZW模型中表明，类似关系也是正确的：WZW标量的边界相关器具有与手性Kač-Moody Currents相关器相同的结构。这是在ADS $ _2 $中的树和一环Witten图的级别上检查的。我们还计算了在ADS $ _2 $上定义的通用$σ$模型中的一些树级相关器，并证明它们仅在出现额外的Kač-Moody对称性的WZW情况下简化。特别是，对对数依赖性对1D交叉比例的4点相关器中的术语仅在WZW点取消。这项工作背后的一个动机是学习如何在2D模型中计算ADS $ _2 $循环校正，这些循环校正与ADS中Wilson Loops on Wilson Loops的操作员的相关器有关的派生相互作用。
Boundary correlators of elementary fields in some 2d conformal field theories defined on AdS$_2$ have a particularly simple structure. For example, the correlators of the Liouville scalar happen to be the same as the correlators of the chiral component of the stress tensor on a plane restricted to the real line. Here we show that an analogous relation is true also in the WZW model: boundary correlators of the WZW scalars have the same structure as the correlators of chiral Kač-Moody currents. This is checked at the level of the tree and one-loop Witten diagrams in AdS$_2$. We also compute some tree-level correlators in a generic $σ$-model defined on AdS$_2$ and show that they simplify only in the WZW case where an extra Kač-Moody symmetry appears. In particular, the terms in 4-point correlators having logarithmic dependence on 1d cross-ratio cancel only at the WZW point. One motivation behind this work is to learn how to compute AdS$_2$ loop corrections in 2d models with derivative interactions related to the study of correlators of operators on Wilson loops in string theory in AdS.
