# Scattering equations and matrices: from Einstein to Yang-Mills, DBI and NLSM

@article{Cachazo2014ScatteringEA,
title={Scattering equations and matrices: from Einstein to Yang-Mills, DBI and NLSM},
author={Freddy Cachazo and Song He and Ellis Ye Yuan},
journal={Journal of High Energy Physics},
year={2014},
volume={2015},
pages={1-43}
}
• Published 10 December 2014
• Mathematics
• Journal of High Energy Physics
A bstractThe tree-level S-matrix of Einstein’s theory is known to have a representation as an integral over the moduli space of punctured spheres localized to the solutions of the scattering equations. In this paper we introduce three operations that can be applied on the integrand in order to produce other theories. Starting in d + M dimensions we use dimensional reduction to construct Einstein-Maxwell with gauge group U(1)M . The second operation turns gravitons into gluons and we call it…
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