Symmetric-group decomposition of SU(N) group-theory constraints on four-, five-, and six-point color-ordered amplitudes

TL;DR

This paper develops a symmetric group-based framework to analyze and derive group-theory constraints on color-ordered amplitudes in SU(N) gauge theory, extending previous results to six-point functions at all loop orders.

Contribution

It introduces a novel symmetric group decomposition method to systematically derive and organize group-theory constraints for multi-point amplitudes in gauge theories.

Findings

Derived constraints for six-point amplitudes at all loop orders.

Decomposed four-, five-, and six-point constraints into irreducible S_n subspaces.

Extended earlier results from four- and five-point cases.

Abstract

Color-ordered amplitudes for the scattering of n particles in the adjoint representation of SU(N) gauge theory satisfy constraints that arise from group theory alone. These constraints break into subsets associated with irreducible representations of the symmetric group S_n, which allows them to be presented in a compact and natural way. Using an iterative approach, we derive the constraints for six-point amplitudes at all loop orders, extending earlier results for n=4 and n=5. We then decompose the four-, five-, and six-point group-theory constraints into their irreducible S_n subspaces. We comment briefly on higher-point two-loop amplitudes.