The Algebraic Structure of the KLT Relations for Gauge and Gravity Tree Amplitudes
We study the Kawai-Lewellen-Tye (KLT) relations for quantum field theory by reformulating it as an isomorphism between two Lie algebras. We also show how explicit formulas for KLT relations arise when studying rational functions on ℳ₀,ₙ, and prove identities that allow for arbitrary rational functio...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2021 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2021
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211426 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | The Algebraic Structure of the KLT Relations for Gauge and Gravity Tree Amplitudes. Hadleigh Frost. SIGMA 17 (2021), 101, 23 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862697233662607360 |
|---|---|
| author | Frost, Hadleigh |
| author_facet | Frost, Hadleigh |
| citation_txt | The Algebraic Structure of the KLT Relations for Gauge and Gravity Tree Amplitudes. Hadleigh Frost. SIGMA 17 (2021), 101, 23 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We study the Kawai-Lewellen-Tye (KLT) relations for quantum field theory by reformulating it as an isomorphism between two Lie algebras. We also show how explicit formulas for KLT relations arise when studying rational functions on ℳ₀,ₙ, and prove identities that allow for arbitrary rational functions to be expanded in any given basis. Via the Cachazo-He-Yuan formulas, these identities also lead to new formulas for gauge and gravity tree amplitudes, including formulas for so-called Bern-Carrasco-Johansson numerators, in the cases of non-linear sigma model and maximal-helicity-violating Yang-Mills amplitudes.
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| first_indexed | 2026-03-18T08:07:33Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211426 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-18T08:07:33Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Frost, Hadleigh 2026-01-02T08:30:23Z 2021 The Algebraic Structure of the KLT Relations for Gauge and Gravity Tree Amplitudes. Hadleigh Frost. SIGMA 17 (2021), 101, 23 pages 1815-0659 2020 Mathematics Subject Classification: 05C05; 17B62; 81T13; 81T30 arXiv:2111.07257 https://nasplib.isofts.kiev.ua/handle/123456789/211426 https://doi.org/10.3842/SIGMA.2021.101 We study the Kawai-Lewellen-Tye (KLT) relations for quantum field theory by reformulating it as an isomorphism between two Lie algebras. We also show how explicit formulas for KLT relations arise when studying rational functions on ℳ₀,ₙ, and prove identities that allow for arbitrary rational functions to be expanded in any given basis. Via the Cachazo-He-Yuan formulas, these identities also lead to new formulas for gauge and gravity tree amplitudes, including formulas for so-called Bern-Carrasco-Johansson numerators, in the cases of non-linear sigma model and maximal-helicity-violating Yang-Mills amplitudes. This article is based on a talk given at the 2020 ‘Algebraic Structures in Perturbative Quantum Field Theory’ conference, in honor of Dirk Kreimer for his 60th birthday. The author thanks Lionel Mason and the referees for their crucial observations and helpful comments. The work is supported by an ERC grant, GALOP ID: 724638. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Algebraic Structure of the KLT Relations for Gauge and Gravity Tree Amplitudes Article published earlier |
| spellingShingle | The Algebraic Structure of the KLT Relations for Gauge and Gravity Tree Amplitudes Frost, Hadleigh |
| title | The Algebraic Structure of the KLT Relations for Gauge and Gravity Tree Amplitudes |
| title_full | The Algebraic Structure of the KLT Relations for Gauge and Gravity Tree Amplitudes |
| title_fullStr | The Algebraic Structure of the KLT Relations for Gauge and Gravity Tree Amplitudes |
| title_full_unstemmed | The Algebraic Structure of the KLT Relations for Gauge and Gravity Tree Amplitudes |
| title_short | The Algebraic Structure of the KLT Relations for Gauge and Gravity Tree Amplitudes |
| title_sort | algebraic structure of the klt relations for gauge and gravity tree amplitudes |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211426 |
| work_keys_str_mv | AT frosthadleigh thealgebraicstructureofthekltrelationsforgaugeandgravitytreeamplitudes AT frosthadleigh algebraicstructureofthekltrelationsforgaugeandgravitytreeamplitudes |