Gauge theories from scattering amplitudes with minimal assumptions

TL;DR

The work shows that the Yang-Mills symmetry for massless spin-1 particles arises from fundamental on-shell principles by analyzing four-point amplitude factorization, without assuming specific three-point coupling properties. A key non-ambiguity condition (NAC) on color-space matrices is derived, establishing a real basis in which the couplings become Hermitian and obey the Jacobi identity, thereby identifying a reductive Lie algebra that generates YM transformations. This framework extends to interactions with matter and to gravity, yielding universal graviton couplings and sector decoupling, while CP invariance emerges as a consequence rather than a prior assumption, at least at tree level for minimal gluon couplings. The approach links on-shell amplitude constraints with symmetry structures via Weinberg’s soft theorems, suggesting a unified, minimal-assumption route to fundamental gauge and gravitational interactions with implications for CP properties and potential anomaly considerations.

Abstract

We revisit the emergence of a Yang-Mills symmetry in theories with massless spin 1 particles from fundamental physical properties of scattering amplitudes. In the standard proofs, some symmetry and reality properties of the coupling constants in three-point amplitudes are assumed. These properties cannot be justified using only three-point amplitudes but we show that they arise as consequences of the consistent factorization of four-particle amplitudes, for particular choices of the particle basis. This applies to self-interactions of massless spin 1 particles and also to their interactions with spin 0 and 1/2 particles. CP invariance is a derived property, not an additional assumption. The situation for gravity interactions is analogous and it is dealt with in the same fashion.