Locality and Unitarity from Singularities and Gauge Invariance

TL;DR

This paper demonstrates that locality and unitarity of tree-level gluon and graviton amplitudes can be derived from gauge invariance, singularity structure, and minimal assumptions, revealing their fundamental interconnectedness.

Contribution

It proves that gauge invariance and locality uniquely determine tree-level amplitudes, and shows how unitarity follows from these principles, extending to other theories like sigma models.

Findings

Gauge invariance and locality fix amplitudes uniquely.

Unitarity emerges from locality and gauge invariance.

Evidence that singularity structures dictate amplitude graph structures.

Abstract

We conjecture that the leading two-derivative tree-level amplitudes for gluons and gravitons can be derived from gauge invariance together with mild assumptions on their singularity structure. Assuming locality (that the singularities are associated with the poles of cubic graphs), we prove that gauge-invariance in just (n-1) particles together with minimal power-counting uniquely fixes the amplitude. Unitarity in the form of factorization then follows from locality and gauge invariance. We also give evidence for a stronger conjecture: assuming only that singularities occur when the sum of a subset of external momenta go on-shell, we show in non-trivial examples that gauge-invariance and power-counting demand a graph structure for singularities. Thus both locality and unitarity emerge from singularities and gauge invariance. Similar statements hold for theories of Goldstone bosons like the non-linear sigma model and Dirac-Born-Infeld, by replacing the condition of gauge invariance with an appropriate degree of vanishing in soft limits.