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

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.

References in corpus (12)

• New Relations for Gauge-Theory Amplitudes
• Minimal Basis for Gauge Theory Amplitudes
• The Momentum Kernel of Gauge and Gravity Theories
• Ambitwistor strings in 4-dimensions
• Combinatorics and Topology of Kawai-Lewellen-Tye Relations
• Gravity from Rational Curves
• Multiparticle SYM equations of motion and pure spinor BRST blocks
• A simple formula for gravitational MHV amplitudes
• Note on graviton MHV amplitudes
• Fundamental BCJ Relation in N=4 SYM From The Connected Formulation
• A Lie bracket for the momentum kernel
• Ambitwistor Strings: Worldsheet Approaches to perturbative Quantum Field Theories

Cited by in corpus (2)

• Tree-level amplitudes from the pure spinor superstring
• Note on graph-based BCJ relation for Berends-Giele currents