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Geometric duality between effective field theories I: scattering amplitudes

Tomas Brauner, Yang Li, Diederik Roest, Tianzhi Wang

TL;DR

This work establishes a geometric duality that connects four prominent EFTs—Yang-Mills-scalar theory, nonlinear sigma models, Dirac-Born-Infeld theory, and the special Galileon—via a covariant, quartic-interaction–driven EoM framework. It identifies two duality chains (YMS↔NLSM and NLSMg↔DBI↔sGal) by matching the second-order equations of tensor currents and composite gauge/gravity sectors, then demonstrates the maps explicitly at the level of tree-level amplitudes, including four-point functions. The results reveal that a common geometric structure governs the dynamics and on-shell amplitudes across these theories, providing a new perspective on flavor-kinematics duality and suggesting routes to apply these ideas to nonrelativistic EFTs and broader duality networks. Overall, the paper offers a covariant, geometry-driven lens to relate seemingly distinct EFTs, with potential implications for exact solutions and extensions of double-copy ideas beyond standard relativistic contexts.

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.

Geometric duality between effective field theories I: scattering amplitudes

TL;DR

This work establishes a geometric duality that connects four prominent EFTs—Yang-Mills-scalar theory, nonlinear sigma models, Dirac-Born-Infeld theory, and the special Galileon—via a covariant, quartic-interaction–driven EoM framework. It identifies two duality chains (YMS↔NLSM and NLSMg↔DBI↔sGal) by matching the second-order equations of tensor currents and composite gauge/gravity sectors, then demonstrates the maps explicitly at the level of tree-level amplitudes, including four-point functions. The results reveal that a common geometric structure governs the dynamics and on-shell amplitudes across these theories, providing a new perspective on flavor-kinematics duality and suggesting routes to apply these ideas to nonrelativistic EFTs and broader duality networks. Overall, the paper offers a covariant, geometry-driven lens to relate seemingly distinct EFTs, with potential implications for exact solutions and extensions of double-copy ideas beyond standard relativistic contexts.

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.

Paper Structure

This paper contains 24 sections, 145 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Yang-Mills-scalar theory
  3. Algebraic structure
  4. Equations of motion
  5. Scattering amplitudes
  6. Nonlinear sigma model
  7. Algebraic structure
  8. Equations of motion
  9. Scattering amplitudes
  10. Including gravity
  11. Dirac-Born-Infeld theory
  12. Algebraic and geometric structure
  13. Equations of motion
  14. Scattering amplitudes
  15. Special Galileon theory
  16. ...and 9 more sections

Figures (2)

  • Figure 1: Sample interaction vertices of the rooted graph representation of the YMS theory. For each vertex, the root is the external leg on the left, whereas the external legs on the right are the leaves. The momenta $p,q$ carried by the leaves are always oriented towards the root.
  • Figure 2: Sample interaction vertices of the rooted graph representation of the NLSM. For each vertex, the root is the external leg on the left, whereas the externals legs on the right are the leaves. The momenta $p,q$ carried by the leaves are always oriented towards the root.