Scattering equations and Kawai-Lewellen-Tye orthogonality

By F. Cachazo, Song He, E. Y. Yuan. 2013

438 citations recorded by the source corpus.

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 paper we identify and study equations relating the kinematic invariants ${s}_{ab}$ and the puncture locations ${\ensuremath{\sigma}}_{c}$, 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 Kawai--Lewellen--Tye (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 KLT bilinear form. We end with comments on possible connections to gauge theory and gravity amplitudes in any dimension and to the high-energy limit of string theory amplitudes.

Subfields: Atomic and Molecular Physics, and Optics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/15144cda24fd94db7a6baf3c37e71a54a0a8025c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Humberto Gomez
2. Song He
3. F. Cachazo
4. N. Arkani-Hamed
5. E. Y. Yuan
6. Yuntao Bai
7. L. Mason
8. Gongwang Yan

In Geometry and Topology

1. Song He
2. F. Cachazo
3. E. Y. Yuan
4. Yuntao Bai
5. N. Arkani-Hamed
6. L. Mason
7. H. Johansson
8. Sebastian Mizera

In Mathematical Physics

1. Song He
2. F. Cachazo
3. E. Y. Yuan
4. L. Mason
5. N. Arkani-Hamed
6. Yuntao Bai
7. H. Johansson
8. Sebastian Mizera

Citations in the corpus

• Einstein-Yang-Mills scattering amplitudes from scattering equations (2014, methodology): “The reason is that the double-copy construction has been shown to be closely related to KLT orthogonality [31, 32] and the CHY representations in [2].”
• Celestial amplitudes and conformal soft theorems (2019, neutral): “, [42, 43]).”
• Λ scattering equations (2016, background): “Some of them are gauge invariance, soft limits, BCJ relations and the existence of KLT formulas [17, 45–55].”
• Scattering forms and the positive geometry of kinematics, color and the worldsheet (2017, background): “Furthermore, recall that the scattering equations [5] relate points in moduli space to points in kinematic space.”
• Color-kinematics duality for QCD amplitudes (2015, background): “The BCJ amplitude relations motivated the discovery of the scattering equations and associated elegant string-like formulas for gauge and gravity tree amplitudes [86–89].”
• Scattering equations and matrices: from Einstein to Yang-Mills, DBI and NLSM (2014, methodology): “One of the main results of [4] is that the matrix m now computed as”
• One-loop amplitudes on the Riemann sphere (2015, methodology): “In the ambitwistor string this follows from KLT orthogonality [15].”
• Extensions of theories from soft limits (2016, background): “Here σab = σa − σb and the scattering equations [20] are given by Ea = ∑”