Scattering equations: real solutions and particles on a line

  title={Scattering equations: real solutions and particles on a line},
  author={Freddy Cachazo and Sebastian Mizera and Guojun Zhang},
  journal={Journal of High Energy Physics},
A bstractWe find n(n − 3)/2-dimensional regions of the space of kinematic invariants, where all the solutions to the scattering equations (the core of the CHY formulation of amplitudes) for n massless particles are real. On these regions, the scattering equations are equivalent to the problem of finding stationary points of n − 3 mutually repelling particles on a finite real interval with appropriate boundary conditions. This identification directly implies that for each of the (n − 3… 
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A compact formula for the complete tree-level S-matrix of pure Yang-Mills and gravity theories in arbitrary spacetime dimensions is presented and Gauge invariance is completely manifest as it follows from a simple property of the Pfaffian.
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A dual formulation of the S Matrix for $$ \mathcal {N} $$ = 4 SYM has recently been presented, where all leading singularities of n-particle Nk−2MHV amplitudes are given as an integral over the
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