SU(N) group-theory constraints on color-ordered five-point amplitudes at all loop orders

Understand

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.