2013/07/10 by Freddy Cachazo, Song He, Ellis Ye Yuan · 2 citations
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1103/physrevlett.113.171601
published as Phys. Rev. Lett. 113, 171601 (2014) · v2: Simpler form for gravity added. Argument below eq. 14 streamlined. 4 pages, 2 columns
arxiv created 2013/07/10 · arxiv updated 2014/10/29
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.