Cosmological scattering equations at tree-level and one-loop
Abstract We recently proposed a formula for tree-level n-point correlators of massive ϕ 4 theory in de Sitter momentum space which consists of an integral over n punctures on the Riemann sphere and differential operators in the future boundary dubbed the cosmological scattering equations. This formu...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-07-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP07(2022)004 |
| _version_ | 1818470906225229824 |
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| author | Humberto Gomez Renann Lipinski Jusinskas Arthur Lipstein |
| author_facet | Humberto Gomez Renann Lipinski Jusinskas Arthur Lipstein |
| author_sort | Humberto Gomez |
| collection | DOAJ |
| description | Abstract We recently proposed a formula for tree-level n-point correlators of massive ϕ 4 theory in de Sitter momentum space which consists of an integral over n punctures on the Riemann sphere and differential operators in the future boundary dubbed the cosmological scattering equations. This formula was explicitly checked up to six points via a map to Witten diagrams using the global residue theorem. In this work we provide further details of these calculations and present an alternative formulation based on a double cover of the Riemann sphere. This framework can be used to derive simple graphical rules for evaluating the integrals more efficiently. Using these rules, we check the validity of our formula up to eight points and sketch the derivation of n-point correlators. Finally, we propose a similar formula for 1-loop n-point correlators in terms of an integral over (n + 2) punctures on the Riemann sphere, which we verify at four points. The 1-loop formula holds for small masses in de Sitter space and arbitrary masses satisfying the Breitenlohner-Freedman bound after Wick-rotating to Anti-de Sitter space. |
| first_indexed | 2024-04-13T21:43:48Z |
| format | Article |
| id | doaj.art-e04b76deeb934930b9ee1c674785a53a |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-13T21:43:48Z |
| publishDate | 2022-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-e04b76deeb934930b9ee1c674785a53a2022-12-22T02:28:39ZengSpringerOpenJournal of High Energy Physics1029-84792022-07-012022714510.1007/JHEP07(2022)004Cosmological scattering equations at tree-level and one-loopHumberto Gomez0Renann Lipinski Jusinskas1Arthur Lipstein2Department of Mathematical Sciences, Durham UniversityInstitute of Physics of the Czech Academy of Sciences & CEICODepartment of Mathematical Sciences, Durham UniversityAbstract We recently proposed a formula for tree-level n-point correlators of massive ϕ 4 theory in de Sitter momentum space which consists of an integral over n punctures on the Riemann sphere and differential operators in the future boundary dubbed the cosmological scattering equations. This formula was explicitly checked up to six points via a map to Witten diagrams using the global residue theorem. In this work we provide further details of these calculations and present an alternative formulation based on a double cover of the Riemann sphere. This framework can be used to derive simple graphical rules for evaluating the integrals more efficiently. Using these rules, we check the validity of our formula up to eight points and sketch the derivation of n-point correlators. Finally, we propose a similar formula for 1-loop n-point correlators in terms of an integral over (n + 2) punctures on the Riemann sphere, which we verify at four points. The 1-loop formula holds for small masses in de Sitter space and arbitrary masses satisfying the Breitenlohner-Freedman bound after Wick-rotating to Anti-de Sitter space.https://doi.org/10.1007/JHEP07(2022)004AdS-CFT CorrespondenceScattering Amplitudes |
| spellingShingle | Humberto Gomez Renann Lipinski Jusinskas Arthur Lipstein Cosmological scattering equations at tree-level and one-loop Journal of High Energy Physics AdS-CFT Correspondence Scattering Amplitudes |
| title | Cosmological scattering equations at tree-level and one-loop |
| title_full | Cosmological scattering equations at tree-level and one-loop |
| title_fullStr | Cosmological scattering equations at tree-level and one-loop |
| title_full_unstemmed | Cosmological scattering equations at tree-level and one-loop |
| title_short | Cosmological scattering equations at tree-level and one-loop |
| title_sort | cosmological scattering equations at tree level and one loop |
| topic | AdS-CFT Correspondence Scattering Amplitudes |
| url | https://doi.org/10.1007/JHEP07(2022)004 |
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