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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.04186 |
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| _version_ | 1866913680236478464 |
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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 |