Geometric duality between effective field theories I: scattering amplitudes

TL;DR

This paper introduces a new duality linking various scalar and gauge theories through a geometric framework, revealing deep connections in their scattering amplitudes.

Contribution

It establishes a novel geometric duality connecting Yang-Mills with scalar theories like the nonlinear sigma model and Dirac-Born-Infeld, using a covariant formulation.

Findings

Unified geometric framework for multiple theories

Explicit duality relations between gauge and scalar theories

Enhanced understanding of scattering amplitude structures

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.