Difference equations and integral families for Witten diagrams

Journal Article · Tue Dec 10 00:00:00 EST 2024 · Journal of High Energy Physics

DOI:https://doi.org/10.1007/JHEP12(2024)070· OSTI ID:3007344

Alaverdian, Mark ^[1]; Herderschee, Aidan ^[2]; Roiban, Radu ^[1]; Teng, Fei ^[1]

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1. Pennsylvania State University, University Park, PA (United States)
2. Institute for Advanced Study, Princeton, NJ (United States); University of Michigan, Ann Arbor, MI (United States)

We show that tree-level and one-loop Mellin space correlators in anti-de Sitter space obey certain difference equations, which are the direct analog to the differential equations for Feynman loop integrals in the flat space. Finite-difference relations, which we refer to as “summation-by-parts relations”, in parallel with the integration-by-parts relations for Feynman loop integrals, are derived to reduce the integrals to a basis. We illustrate the general methodology by explicitly deriving the difference equations and summation-by-parts relations for various tree-level and one-loop Witten diagrams up to the four-point bubble level.

• Research Organization: The Pennsylvania State University, University Park, PA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: SC0019066
• OSTI ID: 3007344
• Journal Information: Journal of High Energy Physics, Journal Name: Journal of High Energy Physics Journal Issue: 12 Vol. 2024; ISSN 1029-8479
• Publisher: Springer Science and Business Media LLC
• Country of Publication: United States
• Language: English

Related Subjects

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Field Theories in Higher Dimensions
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