论文标题
通用旋转Casimir方程及其解决方案
Universal Spinning Casimir Equations and Their Solutions
论文作者
论文摘要
共形块是用于较高维度综合场理论的中心分析工具。我们使用Harish-Chandra的径向组件图来构建通用Casimir微分方程，以在任何维度的欧几里得空间$ d $ d $中旋转共形块。此外，我们还构建了一组差异``转移''操作员，这些操作员允许从某些种子构建Casimir方程的解决方案。在旋转批量共形场理论的四点块的背景下，我们的公式为对任意张量字段和任意尺寸$ d $的现有表达提供了优雅而遥远的概括。通过应用程序来进一步说明我们新的通用旋转块旋转块的力量，以缺陷共形场理论。如果存在co-dimension $ q = 2 $的缺陷，我们能够在缺陷和散装通道中为对称的无纹状体散装张量字段的两点函数构造共形块。这为缺陷引导程序开辟了一个有趣的途径。最后，我们还得出了散装通道中散装式缺陷三分函数的Casimir方程。
Conformal blocks are a central analytic tool for higher dimensional conformal field theory. We employ Harish-Chandra's radial component map to construct universal Casimir differential equations for spinning conformal blocks in any dimension $d$ of Euclidean space. Furthermore, we also build a set of differential ``shifting'' operators that allow to construct solutions of the Casimir equations from certain seeds. In the context of spinning four-point blocks of bulk conformal field theory, our formulas provide an elegant and far reaching generalisation of existing expressions to arbitrary tensor fields and arbitrary dimension $d$. The power of our new universal approach to spinning blocks is further illustrated through applications to defect conformal field theory. In the case of defects of co-dimension $q=2$ we are able to construct conformal blocks for two-point functions of symmetric traceless bulk tensor fields in both the defect and the bulk channel. This opens an interesting avenue for applications to the defect bootstrap. Finally, we also derive the Casimir equations for bulk-bulk-defect three-point functions in the bulk channel.
