Geometric duality between effective field theories I: scattering amplitudes

Abstract

We propose a novel type of duality that connects a sequence of well-known theories with even-multiplicity scalar amplitudes: it relates the Yang-Mills theory coupled to a specific scalar matter sector to the nonlinear sigma model on a symmetric coset space, the (multiflavor) Dirac-Born-Infeld theory, and the special Galileon theory. The duality is manifested with the help of a covariant formulation of the classical equations of motion that features a contact quartic scalar self-coupling combined with propagation on a dynamical background of elementary or composite gauge fields. This is augmented with a set of constitutive relations that reflect the intrinsic or extrinsic geometry of the target space of the theory. The universality of the underlying geometric structure allows for an unambiguous mapping between different theories.

1+41 pages; v2: added a new appendix and otherwise improved the text at several places

References in corpus (26)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• Causality, Analyticity and an IR Obstruction to UV Completion
• New Recursion Relations for Tree Amplitudes of Gluons
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Scattering of Massless Particles in Arbitrary Dimension
• Scattering of Massless Particles: Scalars, Gluons and Gravitons
• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• Scattering Equations and KLT Orthogonality
• The Kinematic Algebra From the Self-Dual Sector
• Effective Field Theories from Soft Limits
• On-Shell Recursion Relations for Effective Field Theories
• A Periodic Table of Effective Field Theories
• A Hidden Symmetry of the Galileon
• Tree-level Amplitudes in the Nonlinear Sigma Model
• Geometric Soft Theorems
• Recursion Relations for Tree-level Amplitudes in the SU(N) Non-linear Sigma Model
• Geometry-Kinematics Duality
• Geometry of Special Galileon
• Lie-algebraic classification of effective theories with enhanced soft limits
• Effective Field Theories on the Jet Bundle
• Effective Field Theory for Spontaneously Broken Symmetry
• Nonrelativistic effective field theories with enhanced symmetries and soft behavior
• Gauged Galileons
• Flavour-kinematics duality for Goldstone modes
• Special Galileon at one loop
• Exceptional nonrelativistic effective field theories with enhanced symmetries