论文标题
缺陷和边界的保形分散关系
Conformal dispersion relations for defects and boundaries
论文作者
论文摘要
我们在缺陷共形场理论中得出了两点相关函数的分散关系。相关器表示为在（单个）不连续性的积分，该不连续性由散装通道操作员产品扩展（OPE）控制。这种非常简单的关系在扰动设置中特别有用，在扰动设置中，不连续性由批量操作员的子集确定。特别是，我们将其应用于$ \ Mathcal {n} = 4 $ Super Yang-Mills理论中的两个手性主要操作员的全息相关器，在有超对称性的Wilson系列的情况下。通过非常简单的计算，我们能够复制并扩展现有结果。我们还提出了第二个关系，该关系从双重不连续性中重建相关器，并由缺陷通道OPE控制。最后，对于Codimension-One缺陷（边界和接口）的情况，我们得出了一个分散关系，该关系从两个OPE通道中接收贡献，并将其应用于$ O（n）$关键模型中的边界相关器。我们重现了$ε^2 $的顺序，从而在$ε$扩展中使用AS输入有限数量的边界CFT数据。
We derive a dispersion relation for two-point correlation functions in defect conformal field theories. The correlator is expressed as an integral over a (single) discontinuity that is controlled by the bulk channel operator product expansion (OPE). This very simple relation is particularly useful in perturbative settings where the discontinuity is determined by a subset of bulk operators. In particular, we apply it to holographic correlators of two chiral primary operators in $\mathcal{N}= 4$ Super Yang-Mills theory in the presence of a supersymmetric Wilson line. With a very simple computation, we are able to reproduce and extend existing results. We also propose a second relation, which reconstructs the correlator from a double discontinuity, and is controlled by the defect channel OPE. Finally, for the case of codimension-one defects (boundaries and interfaces) we derive a dispersion relation which receives contributions from both OPE channels and we apply it to the boundary correlator in the $O(N)$ critical model. We reproduce the order $ε^2$ result in the $ε$-expansion using as input a finite number of boundary CFT data.
