Built on

A. Hodges, A Simple Formula for Gravitational MHV Amplitudes
Original
1930
Earlier work this paper cites.
H. Kawai, D. Lewellen, and S. Tye, A Relation Between Tree Amplitudes of Closed and Open Strings
1986
Earlier work this paper cites.
Cambridge University Press, 1987
M. B. Green, J. Schwarz, and E. Witten, Superstring Theory, Vol. 1: Introduction · 1987
Earlier work this paper cites.
D. J. Gross and P. F. Mende, String Theory Beyond the Planck Scale
1988
Earlier work this paper cites.
R. Kleiss and H. Kuijf, Multi-Gluon Cross-Sections and Five Jet Production at Hadron Colliders
1989
Earlier work this paper cites.
E. Witten, Perturbative Gauge Theory as a String Theory in Twistor Space
2004
Earlier work this paper cites.
R. Roiban, M. Spradlin, and A. Volovich, Tree-Level S-Matrix of Yang-Mills Theory
2004
Earlier work this paper cites.

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2013

Scattering Equations and KLT Orthogonality

Cachazo, Freddy, He, Song, Yuan, Ellis Ye

Understand

Several recent developments point to the fact that rational maps from n-punctured spheres to the null cone of D dimensional momentum space provide a natural language for describing the scattering of massless particles in D dimensions.

In this note we identify and study equations relating the kinematic invariants and the puncture locations, which we call the scattering equations.
We provide an inductive algorithm in the number of particles for their solutions and prove a remarkable property which we call KLT Orthogonality.
In a nutshell, KLT orthogonality means that "Parke-Taylor" vectors constructed from the solutions to the scattering equations are mutually orthogonal with respect to the Kawai-Lewellen-Tye (KLT) bilinear form.

Built on

A. Hodges, A Simple Formula for Gravitational MHV Amplitudes
Original
1930
Earlier work this paper cites.
H. Kawai, D. Lewellen, and S. Tye, A Relation Between Tree Amplitudes of Closed and Open Strings
1986
Earlier work this paper cites.
Cambridge University Press, 1987
M. B. Green, J. Schwarz, and E. Witten, Superstring Theory, Vol. 1: Introduction · 1987
Earlier work this paper cites.
D. J. Gross and P. F. Mende, String Theory Beyond the Planck Scale
1988
Earlier work this paper cites.
R. Kleiss and H. Kuijf, Multi-Gluon Cross-Sections and Five Jet Production at Hadron Colliders
1989
Earlier work this paper cites.
E. Witten, Perturbative Gauge Theory as a String Theory in Twistor Space
2004
Earlier work this paper cites.
R. Roiban, M. Spradlin, and A. Volovich, Tree-Level S-Matrix of Yang-Mills Theory
2004
Earlier work this paper cites.