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Feynman rules for scalar conformal blocks

Fortin, Jean-François and Hoback, Sarah and Ma, Wen-Jie and Parikh, Sarthak and Skiba, Witold (2022) Feynman rules for scalar conformal blocks. Journal of High Energy Physics, 2022 (10). Art. No. 97. ISSN 1029-8479. doi:10.1007/jhep10(2022)097.

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We complete the proof of "Feynman rules" for constructing M-point conformal blocks with external and internal scalars in any topology for arbitrary M in any spacetime dimension by combining the rules for the blocks (based on their Witten diagram interpretation) with the rules for the construction of conformal cross ratios (based on the OPE and "flow diagrams"). The full set of Feynman rules leads to blocks as power series of the hypergeometric type in the conformal cross ratios. We then provide a proof by recursion of the Feynman rules which relies heavily on the first Barnes lemma and the decomposition of the topology of interest in comb structures. Finally, we provide a nine-point example to illustrate the rules.

Item Type:Article
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URLURL TypeDescription
Fortin, Jean-François0000-0002-7813-5015
Ma, Wen-Jie0000-0003-3686-7311
Parikh, Sarthak0000-0002-5831-3873
Skiba, Witold0000-0002-2800-4148
Additional Information:The work of JFF is supported by NSERC. The work of SH is supported by the National Science Foundation Graduate Research Fellowship under Grant No. 2021316516. The work of WJM is supported by the China Scholarship Council and in part by NSERC and FRQNT. The work of SP is supported in part by the Young Faculty Incentive Fellowship from IIT Delhi. The work of WS is supported in part by U.S. DOE HEP grant DE-SC00-17660. SCOAP3 supports the goals of the International Year of Basic Sciences for Sustainable Development.
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
NSF Graduate Research Fellowship2021316516
China Scholarship CouncilUNSPECIFIED
Fonds de recherche du Québec - Nature et technologies (FRQNT)UNSPECIFIED
Department of Energy (DOE)DE-SC0017660
Issue or Number:10
Record Number:CaltechAUTHORS:20221027-402241500.6
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:117633
Deposited By: Research Services Depository
Deposited On:08 Nov 2022 19:32
Last Modified:08 Nov 2022 19:32

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