Geometry-Kinematics 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.

5 pages

References in corpus (5)

• New Relations for Gauge-Theory Amplitudes
• Effective Field Theories from Soft Limits
• Low-Energy Behavior of Gluons and Gravitons from Gauge Invariance
• A Periodic Table of Effective Field Theories
• Soft sub-leading divergences in Yang-Mills amplitudes

Cited by in corpus (17)

• Renormalization of the Standard Model Effective Field Theory from Geometry
• Geometry in Scattering Amplitudes
• Amplitudes, Hopf algebras and the colour-kinematics duality
• Non-perturbative aspects of the self-dual double copy
• On-Shell Covariance of Quantum Field Theory Amplitudes
• Kinematic Hopf algebra for amplitudes and form factors
• Effective Field Theories on the Jet Bundle
• Monolepton production in SMEFT to $\mathcal{O}(1/{\Lambda }^4)$ and beyond
• Jet Bundle Geometry of Scalar Field Theories
• Effective Field Theories as Lagrange Spaces
• Inflationary Adler Conditions
• The Geometric $\nu$SMEFT: Operators and Connections
• Walls, bubbles and doom -- the cosmology of HEFT
• Soft Phonon Theorems
• Field Space Geometry and Nonlinear Supersymmetry
• Geometric duality between effective field theories I: scattering amplitudes
• Residual Symmetries and Their Algebras in the Kerr-Schild Double Copy