论文标题
缺陷CFT的两个点功能
Two Point Functions in Defect CFTs
论文作者
论文摘要
本文旨在成为一种实用的工具，用于构建和调查缺陷共形场理论中的两点相关函数，直接在物理空间，任何两个散装的初选之间或散装主要和缺陷初级之间，并具有任意自旋。尽管几何优雅并且最终是一种更强大的方法，但嵌入空间形式主义在处理混合对称性张量时会变得相当麻烦，尤其是在对物理空间的投影中。本文中的结果提供了一种用于研究通用$ d $二维的保形场理论的两点相关函数的替代方法，该函数具有平坦的$ p $维缺陷和$ d-p = q $ co-dimensions。我们将涉及保守电流，能量动量张量和麦克斯韦场强度的相关函数的一些示例制成，同时分析了由保护和运动方程式产生的约束。还解释了一种获得散装到缺陷相关器的方法。考虑了一些明确的示例：$ \ mathbb {r}^p \ times（{\ mathbb r}^q / {\ mathbb z} _2）$的自由标量理论和楔形上的四维麦克斯韦理论。
This paper is designed to be a practical tool for constructing and investigating two-point correlation functions in defect conformal field theory, directly in physical space, between any two bulk primaries or between a bulk primary and a defect primary, with arbitrary spin. Although geometrically elegant and ultimately a more powerful approach, the embedding space formalism gets rather cumbersome when dealing with mixed symmetry tensors, especially in the projection to physical space. The results in this paper provide an alternative method for studying two-point correlation functions for a generic $d$-dimensional conformal field theory with a flat $p$-dimensional defect and $d-p=q$ co-dimensions. We tabulate some examples of correlation functions involving a conserved current, an energy momentum tensor and a Maxwell field strength, while analysing the constraints arising from conservation and the equations of motion. A method for obtaining bulk-to-defect correlators is also explained. Some explicit examples are considered: free scalar theory on $\mathbb{R}^p \times ({\mathbb R}^q / {\mathbb Z}_2)$ and a free four dimensional Maxwell theory on a wedge.
