From infinity to four dimensions: higher residue pairings and Feynman integrals
Abstract We study a surprising phenomenon in which Feynman integrals in D = 4 − 2ε space-time dimensions as ε → 0 can be fully characterized by their behavior in the opposite limit, ε → ∞. More concretely, we consider vector bundles of Feynman integrals over kinematic spaces, whose connections have...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-02-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP02(2020)159 |
| _version_ | 1818031884685279232 |
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| author | Sebastian Mizera Andrzej Pokraka |
| author_facet | Sebastian Mizera Andrzej Pokraka |
| author_sort | Sebastian Mizera |
| collection | DOAJ |
| description | Abstract We study a surprising phenomenon in which Feynman integrals in D = 4 − 2ε space-time dimensions as ε → 0 can be fully characterized by their behavior in the opposite limit, ε → ∞. More concretely, we consider vector bundles of Feynman integrals over kinematic spaces, whose connections have a polynomial dependence on ε and are known to be governed by intersection numbers of twisted forms. They give rise to differential equations that can be obtained exactly as a truncating expansion in either ε or 1/ε. We use the latter for explicit computations, which are performed by expanding intersection numbers in terms of Saito’s higher residue pairings (previously used in the context of topological Landau-Ginzburg models and mirror symmetry). These pairings localize on critical points of a certain Morse function, which correspond to regions in the loop-momentum space that were previously thought to govern only the large-D physics. The results of this work leverage recent understanding of an analogous situation for moduli spaces of curves, where the α′ → 0 and α′ → ∞ limits of intersection numbers coincide for scattering amplitudes of massless quantum field theories. |
| first_indexed | 2024-12-10T05:58:34Z |
| format | Article |
| id | doaj.art-faf57d59bc0940cf9b4345cbb4b7f5c4 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-10T05:58:34Z |
| publishDate | 2020-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-faf57d59bc0940cf9b4345cbb4b7f5c42022-12-22T01:59:52ZengSpringerOpenJournal of High Energy Physics1029-84792020-02-012020213910.1007/JHEP02(2020)159From infinity to four dimensions: higher residue pairings and Feynman integralsSebastian Mizera0Andrzej Pokraka1Institute for Advanced StudyDepartment of Physics, McGill UniversityAbstract We study a surprising phenomenon in which Feynman integrals in D = 4 − 2ε space-time dimensions as ε → 0 can be fully characterized by their behavior in the opposite limit, ε → ∞. More concretely, we consider vector bundles of Feynman integrals over kinematic spaces, whose connections have a polynomial dependence on ε and are known to be governed by intersection numbers of twisted forms. They give rise to differential equations that can be obtained exactly as a truncating expansion in either ε or 1/ε. We use the latter for explicit computations, which are performed by expanding intersection numbers in terms of Saito’s higher residue pairings (previously used in the context of topological Landau-Ginzburg models and mirror symmetry). These pairings localize on critical points of a certain Morse function, which correspond to regions in the loop-momentum space that were previously thought to govern only the large-D physics. The results of this work leverage recent understanding of an analogous situation for moduli spaces of curves, where the α′ → 0 and α′ → ∞ limits of intersection numbers coincide for scattering amplitudes of massless quantum field theories.http://link.springer.com/article/10.1007/JHEP02(2020)159Scattering AmplitudesDifferential and Algebraic GeometryField Theories in Higher Dimensions |
| spellingShingle | Sebastian Mizera Andrzej Pokraka From infinity to four dimensions: higher residue pairings and Feynman integrals Journal of High Energy Physics Scattering Amplitudes Differential and Algebraic Geometry Field Theories in Higher Dimensions |
| title | From infinity to four dimensions: higher residue pairings and Feynman integrals |
| title_full | From infinity to four dimensions: higher residue pairings and Feynman integrals |
| title_fullStr | From infinity to four dimensions: higher residue pairings and Feynman integrals |
| title_full_unstemmed | From infinity to four dimensions: higher residue pairings and Feynman integrals |
| title_short | From infinity to four dimensions: higher residue pairings and Feynman integrals |
| title_sort | from infinity to four dimensions higher residue pairings and feynman integrals |
| topic | Scattering Amplitudes Differential and Algebraic Geometry Field Theories in Higher Dimensions |
| url | http://link.springer.com/article/10.1007/JHEP02(2020)159 |
| work_keys_str_mv | AT sebastianmizera frominfinitytofourdimensionshigherresiduepairingsandfeynmanintegrals AT andrzejpokraka frominfinitytofourdimensionshigherresiduepairingsandfeynmanintegrals |