Abstract
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.
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Hoback, S., Parikh, S. Dimensional reduction of higher-point conformal blocks. J. High Energ. Phys. 2021, 187 (2021). https://doi.org/10.1007/JHEP03(2021)187
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DOI: https://doi.org/10.1007/JHEP03(2021)187