Dimensional reduction of higher-point conformal blocks
- Creators
- Hoback, Sarah
- Parikh, Sarthak
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.
Additional Information
© 2021 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: November 30, 2020; Accepted: February 9, 2021; Published: March 19, 2021. We thank J.-F. Fortin, W.-J. Ma and W. Skiba for useful discussions.Attached Files
Published - Hoback-Parikh2021_Article_DimensionalReductionOfHigher-p.pdf
Submitted - 2009.12904.pdf
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Additional details
- Eprint ID
- 108543
- Resolver ID
- CaltechAUTHORS:20210324-102102021
- SCOAP3
- Created
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2021-03-24Created from EPrint's datestamp field
- Updated
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2021-03-24Created from EPrint's last_modified field