Geometry-Kinematics Duality

TL;DR

This paper establishes a duality between geometry and kinematics for massless bosons, showing their scattering amplitudes match those of a nonlinear sigma model with a momentum-dependent metric, unifying various soft theorems.

Contribution

It introduces a novel mapping linking geometric and kinematic descriptions of massless bosons, revealing their equivalence to nonlinear sigma models with a unified soft theorem framework.

Findings

Tree-level scattering amplitudes of massless bosons match NLSM amplitudes.

Kinematic geometric structures transform under field redefinitions.

Soft theorems for scalars and photons are unified through this duality.

Abstract

We propose a mapping between geometry and kinematics that implies the classical equivalence of any theory of massless bosons -- including spin and exhibiting arbitrary derivative or potential interactions -- to a nonlinear sigma model (NLSM) with a momentum-dependent metric in field space. From this kinematic metric we construct a corresponding kinematic connection, covariant derivative, and curvature, all of which transform appropriately under general field redefinitions, even including derivatives. We show explicitly how all tree-level on-shell scattering amplitudes of massless bosons are equal to those of the NLSM via the replacement of geometry with kinematics. Lastly, we describe how the recently introduced geometric soft theorem of the NLSM, which universally encodes all leading and subleading soft scalar theorems, also captures the soft photon theorems.