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

TL;DR

This paper derives all-loop order group-theory constraints on five-point color-ordered amplitudes in SU(N) gauge theory, extending known relations from tree and one-loop levels using an iterative method.

Contribution

It introduces a comprehensive iterative approach to derive all-loop order group-theory constraints for five-point amplitudes in SU(N) gauge theory.

Findings

Constraints hold at all loop orders for five-point amplitudes.

Generalizes known tree-level and one-loop relations.

Provides a systematic method for deriving group-theory constraints.

Abstract

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.