Locality and Unitarity from Singularities and Gauge Invariance

TL;DR

This work proposes that locality and unitarity of tree-level Yang-Mills and gravity amplitudes can be derived from on-shell gauge invariance, coupled with mild assumptions on singularity structure. By enforcing gauge invariance on all but one external leg and leveraging soft theorems, the authors show that the amplitudes are uniquely fixed, with unitarity emerging from these constraints; they extend the framework to gravity and the BCJ double-copy, and show analogous results for Goldstone theories via soft limits. They also provide evidence for a stronger conjecture that the graph-structure of singularities may itself emerge from gauge invariance, at least in the non-linear sigma model, with partial progress to higher points. The work connects traditional locality/duality ideas to a perspective where gauge redundancy imposes the essential structure, offering a path toward deeper understanding of spacetime and scattering dynamics.

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.