论文标题
迈向联邦法规规则
Towards Feynman rules for conformal blocks
论文作者
论文摘要
我们推测了一组简单的“ Feynman规则”，用于在$ d $ d $ spacetimes尺寸中构建任何渠道中的$ n $ n $ point Global condormal块，用于外部和交换的标量运算符，用于任意$ n $和$ d $。顶点因素是根据一个，两个或三个变量的月桂菌高几何函数给出的，而Feynman规则则提供了交叉比例力量的显式功率系列扩展。这些规则是根据文献中先前已知的结果猜想的，其中包括四个，五点和六点示例以及$ n $ - 点梳子通道块。我们证明了所有以前已知的案例的规则，以及新拓扑中的七点块和“ OPE通道”中的偶数块。证明依赖于全息方法，特别是标量有效场理论中树级广告图的梅林幅度的Feynman规则，并且很容易适用于任何特定选择的共形块。
We conjecture a simple set of "Feynman rules" for constructing $n$-point global conformal blocks in any channel in $d$ spacetime dimensions, for external and exchanged scalar operators for arbitrary $n$ and $d$. The vertex factors are given in terms of Lauricella hypergeometric functions of one, two or three variables, and the Feynman rules furnish an explicit power-series expansion in powers of cross-ratios. These rules are conjectured based on previously known results in the literature, which include four-, five- and six-point examples as well as the $n$-point comb channel blocks. We prove these rules for all previously known cases, as well as for a seven-point block in a new topology and the even-point blocks in the "OPE channel." The proof relies on holographic methods, notably the Feynman rules for Mellin amplitudes of tree-level AdS diagrams in a scalar effective field theory, and is easily applicable to any particular choice of a conformal block.
