KLT relations from the Einstein-Hilbert Lagrangian

TL;DR

This work demonstrates that KLT relations can be made manifest off-shell by recasting the Einstein-Hilbert action in light-cone gauge through a canonical field redefinition, exposing MHV-like off-shell vertices. At ${\cal O}(\kappa^2)$, the three- and four-point gravity interactions factorize into products of off-shell Yang-Mills MHV vertices, providing an off-shell realization of $M_3^{tree}=A_3^{tree}A_3^{tree}$ and $M_4^{tree}=-i\,s_{12}\,A_4^{tree}A_4^{tree}$. The analysis uses a Rosly-Mansfield–style approach to build a shifted gravity action with a kinetic term in $C,\bar C$ and higher-order interactions, and identifies the necessary field redefinitions to remove terms proportional to the free equations of motion. The results suggest a path to extend KLT factorization beyond on-shell amplitudes and raise questions for loop-level consistency and supersymmetric extensions, such as ${\cal N}=8$ supergravity.

Abstract

The Kawai-Lewellen-Tye (KLT) relations derived from string theory tell us that perturbative gravity amplitudes are the "square" of the corresponding amplitudes in gauge theory. Starting from the light-cone Lagrangian for pure gravity we make these relations manifest off-shell, for three- and four-graviton vertices, at the level of the action.