The KLT relation from the tree formula and permutohedron
Abstract In this paper, we generalize the Nguyen–Spradlin–Volovich–Wen (NSVW) tree formula from the MHV sector to any helicity sector. We find a close connection between the Permutohedron and the KLT relation, and construct a non-trivial mapping between them, linking the amplitudes in the gauge and...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2023-01-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-022-11168-1 |
| _version_ | 1797863718661390336 |
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| author | Qu Cao Liang Zhang |
| author_facet | Qu Cao Liang Zhang |
| author_sort | Qu Cao |
| collection | DOAJ |
| description | Abstract In this paper, we generalize the Nguyen–Spradlin–Volovich–Wen (NSVW) tree formula from the MHV sector to any helicity sector. We find a close connection between the Permutohedron and the KLT relation, and construct a non-trivial mapping between them, linking the amplitudes in the gauge and gravity theories. The gravity amplitude can also be mapped from a determinant followed from the matrix-tree theorem. Besides, we use the binary tree graphs to manifest its Lie structure. In our tree formula, there is an evident Hopf algebra of the permutation group behind the gravity amplitudes. Using the tree formula, we can directly re-derive the soft/collinear limit of the amplitudes. |
| first_indexed | 2024-04-09T22:41:06Z |
| format | Article |
| id | doaj.art-004d573c99404ed294f1e24f586f22b0 |
| institution | Directory Open Access Journal |
| issn | 1434-6052 |
| language | English |
| last_indexed | 2024-04-09T22:41:06Z |
| publishDate | 2023-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-004d573c99404ed294f1e24f586f22b02023-03-22T12:10:22ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522023-01-018311810.1140/epjc/s10052-022-11168-1The KLT relation from the tree formula and permutohedronQu Cao0Liang Zhang1Department of Physics, Zhejiang Institute of Modern Physics, Zhejiang UniversityDepartment of Physics, Zhejiang Institute of Modern Physics, Zhejiang UniversityAbstract In this paper, we generalize the Nguyen–Spradlin–Volovich–Wen (NSVW) tree formula from the MHV sector to any helicity sector. We find a close connection between the Permutohedron and the KLT relation, and construct a non-trivial mapping between them, linking the amplitudes in the gauge and gravity theories. The gravity amplitude can also be mapped from a determinant followed from the matrix-tree theorem. Besides, we use the binary tree graphs to manifest its Lie structure. In our tree formula, there is an evident Hopf algebra of the permutation group behind the gravity amplitudes. Using the tree formula, we can directly re-derive the soft/collinear limit of the amplitudes.https://doi.org/10.1140/epjc/s10052-022-11168-1 |
| spellingShingle | Qu Cao Liang Zhang The KLT relation from the tree formula and permutohedron European Physical Journal C: Particles and Fields |
| title | The KLT relation from the tree formula and permutohedron |
| title_full | The KLT relation from the tree formula and permutohedron |
| title_fullStr | The KLT relation from the tree formula and permutohedron |
| title_full_unstemmed | The KLT relation from the tree formula and permutohedron |
| title_short | The KLT relation from the tree formula and permutohedron |
| title_sort | klt relation from the tree formula and permutohedron |
| url | https://doi.org/10.1140/epjc/s10052-022-11168-1 |
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