论文标题
所有共形块的有效规则
Efficient Rules for All Conformal Blocks
论文作者
论文摘要
我们为计算$ d $ d $ d $ d $ d $ d-d-j的四点整体块的一组通用规则在任意Lorentz表示中的操作员在嵌入空间操作员产品扩展形式上的背景下：1905.00434。有了这些规则，确定任何关注障碍的程序的程序被简化为（1）识别相关投影操作员和张量结构，以及（2）应用保形规则以获取块。为了促进撰写术语的簿记，我们介绍了方便的图表符号。我们提出了几个具体示例，以说明一般过程，并演示和测试规则的明确应用。特别是，我们考虑涉及标量$ s $的四点功能和一些特定的不可约R $，即$ \ langle ssss \ rangle $，$ \ langle sssr \ rangle $，$ \ langle srsr srsr srsr \ rangle \ rangle \ rangle $ and $ \ langle isssr iss a $ ssrr \ rangle ass a a a where wher Fermion），并确定所有可能交换表示的相应块。
We formulate a set of general rules for computing $d$-dimensional four-point global conformal blocks of operators in arbitrary Lorentz representations in the context of the embedding space operator product expansion formalism arXiv:1905.00434. With these rules, the procedure for determining any conformal block of interest is reduced to (1) identifying the relevant projection operators and tensor structures and (2) applying the conformal rules to obtain the blocks. To facilitate the bookkeeping of contributing terms, we introduce a convenient diagrammatic notation. We present several concrete examples to illustrate the general procedure as well as to demonstrate and test the explicit application of the rules. In particular, we consider four-point functions involving scalars $S$ and some specific irreducible representations $R$, namely $\langle SSSS\rangle$, $\langle SSSR\rangle$, $\langle SRSR\rangle$ and $\langle SSRR\rangle$ (where, when allowed, $R$ is a vector or a fermion), and determine the corresponding blocks for all possible exchanged representations.
