论文标题
扩展的雪花频道及以后的七点形条块
Seven-Point Conformal Blocks in the Extended Snowflake Channel and Beyond
论文作者
论文摘要
七点功能具有两个不等的拓扑或通道。梳子通道先前已经计算出来，在这里，我们在$ d $ dimensions中计算扩展雪花通道中的标量形成块。我们的计算取决于差分运算符的已知动作，该操作员在嵌入空间中设置了操作员产品的扩展。扩展的雪花通道中的标量形成块是作为共形的交叉比例中的功率序列扩展而获得的，其系数是超几何类型的三重总和。该三重总和分解为单个总和。单和可以看作是起源于梳子通道，并根据$ {} _ 3f_2 $ - hyphemementric函数给出，而双和来自雪花通道，该雪地频道对应于kampédeFériet函数。我们验证我们的结果满足扩展雪花拓扑的对称特性。此外，我们检查了在多个限制下扩展的雪花共形块的行为与已知结果一致。最后，我们猜测规则导致部分构建标量$ m $ $ $ - 点的共形块。
Seven-point functions have two inequivalent topologies or channels. The comb channel has been computed previously and here we compute scalar conformal blocks in the extended snowflake channel in $d$ dimensions. Our computation relies on the known action of the differential operator that sets up the operator product expansion in embedding space. The scalar conformal blocks in the extended snowflake channel are obtained as a power series expansion in the conformal cross-ratios whose coefficients are a triple sum of the hypergeometric type. This triple sum factorizes into a single sum and a double sum. The single sum can be seen as originating from the comb channel and is given in terms of a ${}_3F_2$-hypergeometric function, while the double sum originates from the snowflake channel which corresponds to a Kampé de Fériet function. We verify that our results satisfy the symmetry properties of the extended snowflake topology. Moreover, we check that the behavior of the extended snowflake conformal blocks under several limits is consistent with known results. Finally, we conjecture rules leading to a partial construction of scalar $M$-point conformal blocks in arbitrary topologies.
