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Dimensional reduction of higher-point conformal blocks

Hoback, Sarah and Parikh, Sarthak (2021) Dimensional reduction of higher-point conformal blocks. Journal of High Energy Physics, 2021 (3). Art. No. 187. ISSN 1029-8479. doi:10.1007/jhep03(2021)187. https://resolver.caltech.edu/CaltechAUTHORS:20210324-102102021

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/jhep03(2021)187DOIArticle
https://arxiv.org/abs/2009.12904arXivDiscussion Paper
ORCID:
AuthorORCID
Parikh, Sarthak0000-0002-5831-3873
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.
Funders:
Funding AgencyGrant Number
SCOAP3UNSPECIFIED
Subject Keywords:Conformal Field Theory; Conformal and W Symmetry
Issue or Number:3
DOI:10.1007/jhep03(2021)187
Record Number:CaltechAUTHORS:20210324-102102021
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210324-102102021
Official Citation: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
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108543
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:24 Mar 2021 19:30
Last Modified:24 Mar 2021 19:30

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