The Algebraic Structure of the KLT Relations for Gauge and Gravity Tree Amplitudes

TL;DR

This paper explores the algebraic structure of KLT relations in gauge and gravity theories, providing new formulas and identities that enhance understanding of tree amplitudes and their algebraic foundations.

Contribution

It introduces an algebraic reformulation of KLT relations as Lie algebra isomorphisms and derives new formulas for gauge and gravity amplitudes using rational functions on moduli space.

Findings

New algebraic identities for rational functions on moduli space

Explicit formulas for gauge and gravity tree amplitudes

Formulas for Bern-Carrasco-Johansson numerators in specific models

Abstract

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 ${\mathcal M}_{0,n}$, and prove identities that allow for arbitrary rational functions to be expanded in any given basis. Via the Cachazo-He-Yuan formulas for, these identities also lead to new formulas for gauge and gravity tree amplitudes, including formulas for so-called Bern-Carrasco-Johansson numerators, in the case of non-linear sigma model and maximal-helicity-violating Yang-Mills amplitudes.