Inverse of the string theory KLT kernel

Abstract

The field theory Kawai-Lewellen-Tye (KLT) kernel, which relates scattering amplitudes of gravitons and gluons, turns out to be the inverse of a matrix whose components are bi-adjoint scalar partial amplitudes. In this note we propose an analogous construction for the string theory KLT kernel. We present simple diagrammatic rules for the computation of the α′-corrected bi-adjoint scalar amplitudes that are exact in α′. We find compact expressions in terms of graphs, where the standard Feynman propagators 1/p2 are replaced by either 1/sin(πα′p2/2) or 1/tan(πα′p2/2), as determined by a recursive procedure. We demonstrate how the same object can be used to conveniently expand open string partial amplitudes in a BCJ basis.