KLT relations from the Einstein–Hilbert Lagrangian

Sudarshan Ananth,Stefan Theisen

doi:10.1016/j.physletb.2007.07.003

Sudarshan Ananth, Stefan Theisen

Open Access

https://doi.org/10.1016/j.physletb.2007.07.003

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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.

Highlights

The Kawai–Lewellen–Tye (KLT) relations relate tree-level amplitudes in closed and open string theories [1]
The shifted Lagrangian is not the sum of maximally helicity violating (MHV)-vertices, the off-shell KLT relations, to the order examined in this Letter, are manifest
The hope is that a similar field redefinition in pure gravity will generate interaction terms which make KLT factorization manifest

Summary

Introduction

The Kawai–Lewellen–Tye (KLT) relations relate tree-level amplitudes in closed and open string theories [1]. The KLT relations apply only at the tree-level they have been used, with great success, in conjunction with unitarity based methods to derive loop amplitudes in gravity [2,5]. These relations have proven invaluable in studying the ultraviolet properties of N = 8 supergravity [6]. The question of whether the KLT relations are valid only for on-shell amplitudes or, more generally, at the level of the Lagrangian remains open [7] This is the issue we focus on in this Letter. The shifted Lagrangian is not the sum of MHV-vertices, the off-shell KLT relations, to the order examined in this Letter, are manifest

Yang–Mills

Gravity in light-cone gauge

The perturbative expansion

The field redefinition

The shifted gravity action