论文标题
所有全球一维更高的共形块
All Global One- and Two-Dimensional Higher-Point Conformal Blocks
论文作者
论文摘要
我们介绍了一套完整的规则，以直接表达所有$ m $ $ - 点的共形块中的一维形成条形理论，而不论拓扑是不论拓扑。 $ M $ - 点的共形块是一些精心挑选的保形交叉比例中的功率系列扩展。然后，我们在已知的位置空间运营商产品扩展的帮助下，建设性地证明了任何拓扑的规则。为此，我们首先计算位置空间操作员产品扩展对位置空间最通用功能的作用，该功能与共形场理论相关。这些结果提供了所有拓扑中所有$ m $ $ m $ - 点的共形块，其中包括任意外部和外部准主要操作员（包括二维任意旋转）。
We introduce a full set of rules to directly express all $M$-point conformal blocks in one- and two-dimensional conformal field theories, irrespective of the topology. The $M$-point conformal blocks are power series expansion in some carefully-chosen conformal cross-ratios. We then prove the rules for any topology constructively with the help of the known position space operator product expansion. To this end, we first compute the action of the position space operator product expansion on the most general function of position space coordinates relevant to conformal field theory. These results provide the complete knowledge of all $M$-point conformal blocks with arbitrary external and internal quasi-primary operators (including arbitrary spins in two dimensions) in any topology.
