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...

Full description

Saved in:
Bibliographic Details
Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2021
Main Author: Frost, Hadleigh
Format: Article
Language:English
Published: Інститут математики НАН України 2021
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/211426
Tags: Add Tag
No Tags, Be the first to tag this record!
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

Institution

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.
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