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The double copy effective action: a quantum (chromodynamics) approach to space-time

John Joseph M. Carrasco, Suna Zekioglu

TL;DR

The paper tackles constructing local operator content and effective actions directly from gauge-theory, color-dual, all-multiplicity tree-level amplitudes via the double-copy principle. It introduces a promotion map that turns color-dual numerators into quantum operators and isolates novel $m$-point contact terms through a generalized maximal-cut procedure. Applied to YM and Einstein gravity, the method yields a constructive operator expansion of $\sqrt{-g}R$ from factorized gauge-theory data and naturally extends to higher-derivative operators motivated by $Z$-theory and open string amplitudes. This framework generalizes color-kinematics duality from amplitudes to actions, providing a practical, automatable route from on-shell data to double-copy-compatible effective actions and a deeper operator-level link between gauge theories and gravity.

Abstract

Conventional Lagrangian formulations of gauge and gravity theories emphasize compactness and off-shell symmetry. This often obscures the structure of on-shell physical observables. In this work, we present a constructive framework that elevates gauge-invariant scattering amplitudes to the defining data for quantum field theory actions, including effective field theories. Focusing on double-copy theories, we promote color-dual amplitude numerators to quantum operators. This enables the systematic identification of novel local operator content at each multiplicity and the construction of double-copy-compatible actions. By applying this framework to the well-established double-copy relationship between Einstein gravity and Yang-Mills theory, which holds for all-multiplicity tree-level amplitudes, we demonstrate a systematic path to constructing the operator expansion of $\sqrt{-g}R$ from factorized gauge-theory components. This clarifies how gravitational interactions can be understood as emerging from simpler gauge-theoretic structures at the action level. This formalism extends color-kinematics duality from amplitude data to operator constructions, naturally realizing the double copy at the level of actions and asymptotic quantum states. We illustrate the method with Yang-Mills theory, Einstein gravity, and its application to generating higher-derivative operators inspired by Z-theory and open superstring amplitudes. This work provides a concrete bridge between structured amplitudes and effective actions, offering a physically grounded alternative to traditional EFT basis-building. It reveals at the operator level deep structural connections between gauge theory and gravity (connections long recognized in scattering amplitudes) from fundamental interactions to their quantum state descriptions and higher-derivative extensions.

The double copy effective action: a quantum (chromodynamics) approach to space-time

TL;DR

The paper tackles constructing local operator content and effective actions directly from gauge-theory, color-dual, all-multiplicity tree-level amplitudes via the double-copy principle. It introduces a promotion map that turns color-dual numerators into quantum operators and isolates novel -point contact terms through a generalized maximal-cut procedure. Applied to YM and Einstein gravity, the method yields a constructive operator expansion of from factorized gauge-theory data and naturally extends to higher-derivative operators motivated by -theory and open string amplitudes. This framework generalizes color-kinematics duality from amplitudes to actions, providing a practical, automatable route from on-shell data to double-copy-compatible effective actions and a deeper operator-level link between gauge theories and gravity.

Abstract

Conventional Lagrangian formulations of gauge and gravity theories emphasize compactness and off-shell symmetry. This often obscures the structure of on-shell physical observables. In this work, we present a constructive framework that elevates gauge-invariant scattering amplitudes to the defining data for quantum field theory actions, including effective field theories. Focusing on double-copy theories, we promote color-dual amplitude numerators to quantum operators. This enables the systematic identification of novel local operator content at each multiplicity and the construction of double-copy-compatible actions. By applying this framework to the well-established double-copy relationship between Einstein gravity and Yang-Mills theory, which holds for all-multiplicity tree-level amplitudes, we demonstrate a systematic path to constructing the operator expansion of from factorized gauge-theory components. This clarifies how gravitational interactions can be understood as emerging from simpler gauge-theoretic structures at the action level. This formalism extends color-kinematics duality from amplitude data to operator constructions, naturally realizing the double copy at the level of actions and asymptotic quantum states. We illustrate the method with Yang-Mills theory, Einstein gravity, and its application to generating higher-derivative operators inspired by Z-theory and open superstring amplitudes. This work provides a concrete bridge between structured amplitudes and effective actions, offering a physically grounded alternative to traditional EFT basis-building. It reveals at the operator level deep structural connections between gauge theory and gravity (connections long recognized in scattering amplitudes) from fundamental interactions to their quantum state descriptions and higher-derivative extensions.

Paper Structure

This paper contains 3 sections, 3 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Review
  3. Color-dual representations

Figures (2)

  • Figure 1: From amplitudes to operators. The operator promotion procedure begins with a color-dual amplitude, reduces to a basis of cubic graphs using Jacobi identities, isolates local contact terms (e.g., via maximal cut 2), promotes each numerator to a field-space operator, and assembles the resulting operators into the effective action. The structure is preserved under double copy.
  • Figure 2: