SU(N) group-theory constraints on color-ordered five-point amplitudes at   all loop orders
  Color-ordered amplitudes for the scattering of n particles in the adjoint representation of SU(N) gauge theory satisfy constraints arising solely from group theory. We derive these constraints for n=5 at all loop orders using an iterative approach. These constraints generalize well-known tree-level and one-loop group theory relations. 
Alexander C. Edison and Stephen G. Naculich
hep-th hep-ph