Scattering of Massless Particles in Arbitrary Dimensions
Abstract
We present a compact formula for the complete tree-level S-matrix of pure Yang-Mills 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 dimension-independent 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 Yang-Mills 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
- E-Print:
- v2: Simpler form for gravity added. Argument below eq. 14 streamlined. 4 pages, 2 columns