How tropical are seven- and eight-particle amplitudes?
Abstract We study tropical Grassmanians Tr(k, n) in relation to cluster algebras, and assess their applicability to n-particle amplitudes for n = 7, 8. In N $$ \mathcal{N} $$ = 4 super Yang-Mills theory, we first show that while the totally positive part of Tr(4, 7) may encompass the iterated discon...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-08-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP08(2020)005 |
| _version_ | 1828785109771223040 |
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| author | Niklas Henke Georgios Papathanasiou |
| author_facet | Niklas Henke Georgios Papathanasiou |
| author_sort | Niklas Henke |
| collection | DOAJ |
| description | Abstract We study tropical Grassmanians Tr(k, n) in relation to cluster algebras, and assess their applicability to n-particle amplitudes for n = 7, 8. In N $$ \mathcal{N} $$ = 4 super Yang-Mills theory, we first show that while the totally positive part of Tr(4, 7) may encompass the iterated discontinuity structure of the seven-point Maximally Helicity Violating (MHV) amplitude, it is too small for the Next-to-MHV helicity configuration. Then, using Tr(4, 8) we propose a finite set of 356 cluster A $$ \mathcal{A} $$ -coordinates expected to contain the rational symbol letters of the eight-particle MHV amplitude, and discuss how the remaining square-root letters may be obtained from limits of infinite mutation sequences. Finally, we use a triangulation of the totally positive part of Tr(3, 8) to obtain the associated generalised biadjoint scalar amplitude in a form containing a near-minimal amount of spurious poles. |
| first_indexed | 2024-12-11T23:45:02Z |
| format | Article |
| id | doaj.art-b0dd7382c44f4e459244e14549ac5410 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-11T23:45:02Z |
| publishDate | 2020-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-b0dd7382c44f4e459244e14549ac54102022-12-22T00:45:38ZengSpringerOpenJournal of High Energy Physics1029-84792020-08-012020815010.1007/JHEP08(2020)005How tropical are seven- and eight-particle amplitudes?Niklas Henke0Georgios Papathanasiou1DESY Theory Group, DESY HamburgDESY Theory Group, DESY HamburgAbstract We study tropical Grassmanians Tr(k, n) in relation to cluster algebras, and assess their applicability to n-particle amplitudes for n = 7, 8. In N $$ \mathcal{N} $$ = 4 super Yang-Mills theory, we first show that while the totally positive part of Tr(4, 7) may encompass the iterated discontinuity structure of the seven-point Maximally Helicity Violating (MHV) amplitude, it is too small for the Next-to-MHV helicity configuration. Then, using Tr(4, 8) we propose a finite set of 356 cluster A $$ \mathcal{A} $$ -coordinates expected to contain the rational symbol letters of the eight-particle MHV amplitude, and discuss how the remaining square-root letters may be obtained from limits of infinite mutation sequences. Finally, we use a triangulation of the totally positive part of Tr(3, 8) to obtain the associated generalised biadjoint scalar amplitude in a form containing a near-minimal amount of spurious poles.http://link.springer.com/article/10.1007/JHEP08(2020)0051/N ExpansionExtended SupersymmetryScattering AmplitudesSupersymmetric Gauge Theory |
| spellingShingle | Niklas Henke Georgios Papathanasiou How tropical are seven- and eight-particle amplitudes? Journal of High Energy Physics 1/N Expansion Extended Supersymmetry Scattering Amplitudes Supersymmetric Gauge Theory |
| title | How tropical are seven- and eight-particle amplitudes? |
| title_full | How tropical are seven- and eight-particle amplitudes? |
| title_fullStr | How tropical are seven- and eight-particle amplitudes? |
| title_full_unstemmed | How tropical are seven- and eight-particle amplitudes? |
| title_short | How tropical are seven- and eight-particle amplitudes? |
| title_sort | how tropical are seven and eight particle amplitudes |
| topic | 1/N Expansion Extended Supersymmetry Scattering Amplitudes Supersymmetric Gauge Theory |
| url | http://link.springer.com/article/10.1007/JHEP08(2020)005 |
| work_keys_str_mv | AT niklashenke howtropicalaresevenandeightparticleamplitudes AT georgiospapathanasiou howtropicalaresevenandeightparticleamplitudes |