Dimensional reduction of higher-point conformal blocks

A bstract Recently, with the help of Parisi-Sourlas supersymmetry an intriguing relation was found expressing four-point scalar conformal block a ( d ? 2)-dimensional CFT in terms five-term linear combination blocks -dimensional CFT, constant coefficients. We extend this dimensional reduction to all higher-point arbitrary topology restricted exchanges. show that coefficients appearing finite term obey interesting factorization property allowing them be determined certain graphical Feynman-like rules and associated set vertex edge factors. Notably, these can fully by considering explicit power-series representation just three particular blocks: block, five-point six-point so-called OPE/snowflake topology. In principle, method applied obtain arbitrary-point spinning exchanges as well. also how systematically partial waves higher-points.