Scattering of massless particles in arbitrary dimensions.
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.
Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.
Freddy
F
Cachazo
Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada and School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540, USA.
Song
S
He
Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada and Department of Physics & Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
Ellis Ye
EY
Yuan