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Main Authors: Alaverdian, Mark, Herderschee, Aidan, Roiban, Radu, Teng, Fei
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2406.04186
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author Alaverdian, Mark
Herderschee, Aidan
Roiban, Radu
Teng, Fei
author_facet Alaverdian, Mark
Herderschee, Aidan
Roiban, Radu
Teng, Fei
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2406_04186
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Difference Equations and Integral Families for Witten Diagrams
Alaverdian, Mark
Herderschee, Aidan
Roiban, Radu
Teng, Fei
High Energy Physics - Theory
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.
title Difference Equations and Integral Families for Witten Diagrams
topic High Energy Physics - Theory
url https://arxiv.org/abs/2406.04186