Difference equations and integral families for Witten diagrams
Abstract 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-pa...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-12-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP12(2024)070 |
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| author | Mark Alaverdian Aidan Herderschee Radu Roiban Fei Teng |
| author_facet | Mark Alaverdian Aidan Herderschee Radu Roiban Fei Teng |
| author_sort | Mark Alaverdian |
| collection | DOAJ |
| description | Abstract 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 | Article |
| id | doaj-art-2c51855b59404daa95ccd4bd9266fae5 |
| institution | OA Journals |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-2c51855b59404daa95ccd4bd9266fae52025-08-20T01:59:43ZengSpringerOpenJournal of High Energy Physics1029-84792024-12-0120241214410.1007/JHEP12(2024)070Difference equations and integral families for Witten diagramsMark Alaverdian0Aidan Herderschee1Radu Roiban2Fei Teng3Department of Physics, Pennsylvania State UniversityInstitute for Advanced StudyDepartment of Physics, Pennsylvania State UniversityDepartment of Physics, Pennsylvania State UniversityAbstract 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.https://doi.org/10.1007/JHEP12(2024)070AdS-CFT CorrespondenceField Theories in Higher DimensionsScattering Amplitudes |
| spellingShingle | Mark Alaverdian Aidan Herderschee Radu Roiban Fei Teng Difference equations and integral families for Witten diagrams Journal of High Energy Physics AdS-CFT Correspondence Field Theories in Higher Dimensions Scattering Amplitudes |
| title | Difference equations and integral families for Witten diagrams |
| title_full | Difference equations and integral families for Witten diagrams |
| title_fullStr | Difference equations and integral families for Witten diagrams |
| title_full_unstemmed | Difference equations and integral families for Witten diagrams |
| title_short | Difference equations and integral families for Witten diagrams |
| title_sort | difference equations and integral families for witten diagrams |
| topic | AdS-CFT Correspondence Field Theories in Higher Dimensions Scattering Amplitudes |
| url | https://doi.org/10.1007/JHEP12(2024)070 |
| work_keys_str_mv | AT markalaverdian differenceequationsandintegralfamiliesforwittendiagrams AT aidanherderschee differenceequationsandintegralfamiliesforwittendiagrams AT raduroiban differenceequationsandintegralfamiliesforwittendiagrams AT feiteng differenceequationsandintegralfamiliesforwittendiagrams |