Scattering of Massless Particles in Arbitrary Dimensions
Abstract
We present a compact formula for the complete treelevel Smatrix of pure YangMills and gravity theories in arbitrary spacetime dimensions. The new formula for the scattering of n particles is given by an integral over the positions of n points on a sphere restricted to satisfy a dimensionindependent set of equations. The integrand is constructed using the reduced Pfaffian of a 2n ×2n matrix, Ψ, 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 YangMills integrand. Gauge invariance is completely manifest as it follows from a simple property of the Pfaffian.
 Publication:

Physical Review Letters
 Pub Date:
 October 2014
 DOI:
 10.1103/PhysRevLett.113.171601
 arXiv:
 arXiv:1307.2199
 Bibcode:
 2014PhRvL.113q1601C
 Keywords:

 11.10.Kk;
 11.15.Bt;
 11.55.Bq;
 Field theories in dimensions other than four;
 General properties of perturbation theory;
 Analytic properties of S matrix;
 High Energy Physics  Theory
 EPrint:
 v2: Simpler form for gravity added. Argument below eq. 14 streamlined. 4 pages, 2 columns