论文标题
较高的共形块的尺寸降低
Dimensional reduction of higher-point conformal blocks
论文作者
论文摘要
最近，在巴黎 - 苏拉斯超对称性的帮助下，发现了有趣的关系，表达了A（d-2）维CFT的四点标量形成块，该块以恒定系数为恒定的D-二维CFT的五项线性组合，具有恒定系数。我们将这种维度还原关系扩展到所有限于标量交换的任意拓扑的所有高点标量形成块。我们表明，在有限项更高点降低中出现的恒定系数遵守有趣的分解属性，从而可以根据某些图形Feynman样规则和相关的有限顶点和边缘因子确定它们。值得注意的是，这些规则可以通过考虑仅三个特定的共形块的显式功率序列表示：四点盖帽，五点盖帽和所谓的OPE/Snowflake拓扑的六分障碍。原则上，可以应用此方法来获得随着旋转交换的共形块的任意尺寸降低。我们还展示了如何系统地扩展保形部分波的维度还原关系到更高点。
Recently, with the help of Parisi-Sourlas supersymmetry an intriguing relation was found expressing the four-point scalar conformal block of a (d-2)-dimensional CFT in terms of a five-term linear combination of blocks of a d-dimensional CFT, with constant coefficients. We extend this dimensional reduction relation to all higher-point scalar conformal blocks of arbitrary topology restricted to scalar exchanges. We show that the constant coefficients appearing in the finite term higher-point dimensional reduction obey an interesting factorization property allowing them to be determined in terms of certain graphical Feynman-like rules and the associated finite set of vertex and edge factors. Notably, these rules can be fully determined by considering the explicit power-series representation of just three particular conformal blocks: the four-point block, the five-point block and the six-point block of the so-called OPE/snowflake topology. In principle, this method can be applied to obtain the arbitrary-point dimensional reduction of conformal blocks with spinning exchanges as well. We also show how to systematically extend the dimensional reduction relation of conformal partial waves to higher-points.
