Geometry-Kinematics Duality

Understand

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.