论文标题
雪花频道中的六点形块
Six-Point Conformal Blocks in the Snowflake Channel
论文作者
论文摘要
我们在操作员产品扩展允许的两个可能的拓扑中计算了$ D $二维标量六点共形块。我们的计算是嵌入太空运营商产品扩展形式主义的简单应用。梳子通道中的标量六点共形块已经确定了不久前，我们在这里介绍了剩余的不相等拓扑中标量六点共形块的第一个明确计算。出于明显的原因，我们将另一个拓扑结构为雪花通道。带有标量外部和交换运算符的标量共构块作为共形交叉比例中的功率序列扩展表示，其中功率系列的系数作为超几何类型的双重总和。在梳子通道中，双和可作为两个$ {} _ 3f_2 $ - hyphemementric函数的产物表达。在雪花通道中，双和可作为kampédeFériet函数表达，其中两个总和都交织在一起，不能分解。我们通过验证它们在对称性下的一致性并采取几个限制以减少已知结果的限制来检查我们的结果，主要是在任意时空维度中标量五点共形块。
We compute $d$-dimensional scalar six-point conformal blocks in the two possible topologies allowed by the operator product expansion. Our computation is a simple application of the embedding space operator product expansion formalism developed recently. Scalar six-point conformal blocks in the comb channel have been determined not long ago, and we present here the first explicit computation of the scalar six-point conformal blocks in the remaining inequivalent topology. For obvious reason, we dub the other topology the snowflake channel. The scalar conformal blocks, with scalar external and exchange operators, are presented as a power series expansion in the conformal cross-ratios, where the coefficients of the power series are given as a double sum of the hypergeometric type. In the comb channel, the double sum is expressible as a product of two ${}_3F_2$-hypergeometric functions. In the snowflake channel, the double sum is expressible as a Kampé de Fériet function where both sums are intertwined and cannot be factorized. We check our results by verifying their consistency under symmetries and by taking several limits reducing to known results, mostly to scalar five-point conformal blocks in arbitrary spacetime dimensions.
