Freddy Cachazo, Song He, Ellis Ye Yuan
We present a compact formula for the complete tree-level S-matrix of pure Yang-Mills and gravity theories in arbitrary spacetime dimension. The new formula for the scattering of n particles is given by an integral over the position of n points on a sphere restricted to satisfy a dimension-independent set of equations. The integrand is constructed using the reduced Pfaffian of a 2n by 2n matrix that depends on momenta and polarization vectors. Gauge invariance is completely manifest as it follows from a simple property of the Pfaffian.
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http://arxiv.org/abs/1307.2199
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