Scattering of Massless Particles in Arbitrary Dimension
Abstract
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. In its simplest form, the gravity integrand is a reduced determinant which is the square of the Pfaffian in the Yang-Mills integrand. Gauge invariance is completely manifest as it follows from a simple property of the Pfaffian.
Cite
@article{arxiv.1307.2199,
title = {Scattering of Massless Particles in Arbitrary Dimension},
author = {Freddy Cachazo and Song He and Ellis Ye Yuan},
journal= {arXiv preprint arXiv:1307.2199},
year = {2014}
}
Comments
v2: Simpler form for gravity added. Argument below eq. 14 streamlined. 4 pages, 2 columns