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Towards Feynman rules for conformal blocks

Hoback, Sarah and Parikh, Sarthak (2021) Towards Feynman rules for conformal blocks. Journal of High Energy Physics, 2021 (1). Art. No. 5. ISSN 1029-8479. https://resolver.caltech.edu/CaltechAUTHORS:20210107-131434378

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Abstract

We conjecture a simple set of “Feynman rules” for constructing n-point global conformal blocks in any channel in d spacetime dimensions, for external and exchanged scalar operators for arbitrary n and d. The vertex factors are given in terms of Lauricella hypergeometric functions of one, two or three variables, and the Feynman rules furnish an explicit power-series expansion in powers of cross-ratios. These rules are conjectured based on previously known results in the literature, which include four-, five- and six-point examples as well as the n-point comb channel blocks. We prove these rules for all previously known cases, as well as two new ones: the seven-point block in a new topology, and all even-point blocks in the “OPE channel.” The proof relies on holographic methods, notably the Feynman rules for Mellin amplitudes of tree-level AdS diagrams in a scalar effective field theory, and is easily applicable to any particular choice of a conformal block beyond those considered in this paper.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/jhep01(2021)005DOIArticle
https://arxiv.org/abs/2006.14736arXivDiscussion Paper
ORCID:
AuthorORCID
Parikh, Sarthak0000-0002-5831-3873
Additional Information:© 2020 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: July 22, 2020; Revised: October 24, 2020; Accepted: November 16, 2020; Published: January 4, 2021. The work of S. H. was partially supported by the SCS Summer Research Grant, by the Pomona RAISE Grant, and by Caltech’s Visiting Undergraduate Research Program (VURP).
Funders:
Funding AgencyGrant Number
Pomona CollegeUNSPECIFIED
CaltechUNSPECIFIED
Subject Keywords:Conformal Field Theory; AdS-CFT Correspondence; Conformal and W Symmetry
Issue or Number:1
Record Number:CaltechAUTHORS:20210107-131434378
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210107-131434378
Official Citation:Hoback, S., Parikh, S. Towards Feynman rules for conformal blocks. J. High Energ. Phys. 2021, 5 (2021). https://doi.org/10.1007/JHEP01(2021)005
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:107366
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:08 Jan 2021 17:48
Last Modified:08 Jan 2021 17:48

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