Comments on all-loop constraints for scattering amplitudes and Feynman integrals
Abstract We comment on the status of “Steinmann-like” constraints, i.e. all-loop constraints on consecutive entries of the symbol of scattering amplitudes and Feynman integrals in planar N $$ \mathcal{N} $$ = 4 super-Yang-Mills, which have been crucial for the recent progress of the bootstrap progra...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-01-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP01(2022)073 |
| _version_ | 1798026463366086656 |
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| author | Song He Zhenjie Li Qinglin Yang |
| author_facet | Song He Zhenjie Li Qinglin Yang |
| author_sort | Song He |
| collection | DOAJ |
| description | Abstract We comment on the status of “Steinmann-like” constraints, i.e. all-loop constraints on consecutive entries of the symbol of scattering amplitudes and Feynman integrals in planar N $$ \mathcal{N} $$ = 4 super-Yang-Mills, which have been crucial for the recent progress of the bootstrap program. Based on physical discontinuities and Steinmann relations, we first summarize all possible double discontinuities (or first-two-entries) for (the symbol of) amplitudes and integrals in terms of dilogarithms, generalizing well-known results for n = 6, 7 to all multiplicities. As our main result, we find that extended-Steinmann relations hold for all finite integrals that we have checked, including various ladder integrals, generic double-pentagon integrals, as well as finite components of two-loop NMHV amplitudes for any n; with suitable normalization such as minimal subtraction, they hold for n = 8 MHV amplitudes at three loops. We find interesting cancellation between contributions from rational and algebraic letters, and for the former we have also tested cluster-adjacency conditions using the so-called Sklyanin brackets. Finally, we propose a list of possible last-two-entries for MHV amplitudes up to 9 points derived from Q ¯ $$ \overline{Q} $$ equations, which can be used to reduce the space of functions for higher-point MHV amplitudes. |
| first_indexed | 2024-04-11T18:35:54Z |
| format | Article |
| id | doaj.art-de1d7e0238c7432e964248c1f2a667eb |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-11T18:35:54Z |
| publishDate | 2022-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-de1d7e0238c7432e964248c1f2a667eb2022-12-22T04:09:18ZengSpringerOpenJournal of High Energy Physics1029-84792022-01-012022112410.1007/JHEP01(2022)073Comments on all-loop constraints for scattering amplitudes and Feynman integralsSong He0Zhenjie Li1Qinglin Yang2School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCASCAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of SciencesCAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of SciencesAbstract We comment on the status of “Steinmann-like” constraints, i.e. all-loop constraints on consecutive entries of the symbol of scattering amplitudes and Feynman integrals in planar N $$ \mathcal{N} $$ = 4 super-Yang-Mills, which have been crucial for the recent progress of the bootstrap program. Based on physical discontinuities and Steinmann relations, we first summarize all possible double discontinuities (or first-two-entries) for (the symbol of) amplitudes and integrals in terms of dilogarithms, generalizing well-known results for n = 6, 7 to all multiplicities. As our main result, we find that extended-Steinmann relations hold for all finite integrals that we have checked, including various ladder integrals, generic double-pentagon integrals, as well as finite components of two-loop NMHV amplitudes for any n; with suitable normalization such as minimal subtraction, they hold for n = 8 MHV amplitudes at three loops. We find interesting cancellation between contributions from rational and algebraic letters, and for the former we have also tested cluster-adjacency conditions using the so-called Sklyanin brackets. Finally, we propose a list of possible last-two-entries for MHV amplitudes up to 9 points derived from Q ¯ $$ \overline{Q} $$ equations, which can be used to reduce the space of functions for higher-point MHV amplitudes.https://doi.org/10.1007/JHEP01(2022)073Scattering AmplitudesSupersymmetric Gauge Theory |
| spellingShingle | Song He Zhenjie Li Qinglin Yang Comments on all-loop constraints for scattering amplitudes and Feynman integrals Journal of High Energy Physics Scattering Amplitudes Supersymmetric Gauge Theory |
| title | Comments on all-loop constraints for scattering amplitudes and Feynman integrals |
| title_full | Comments on all-loop constraints for scattering amplitudes and Feynman integrals |
| title_fullStr | Comments on all-loop constraints for scattering amplitudes and Feynman integrals |
| title_full_unstemmed | Comments on all-loop constraints for scattering amplitudes and Feynman integrals |
| title_short | Comments on all-loop constraints for scattering amplitudes and Feynman integrals |
| title_sort | comments on all loop constraints for scattering amplitudes and feynman integrals |
| topic | Scattering Amplitudes Supersymmetric Gauge Theory |
| url | https://doi.org/10.1007/JHEP01(2022)073 |
| work_keys_str_mv | AT songhe commentsonallloopconstraintsforscatteringamplitudesandfeynmanintegrals AT zhenjieli commentsonallloopconstraintsforscatteringamplitudesandfeynmanintegrals AT qinglinyang commentsonallloopconstraintsforscatteringamplitudesandfeynmanintegrals |