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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <msqrt> <mrow> <mo>−</mo> <mi>g</mi> </mrow> </msqrt> <mi>R</mi> </math></EquationSource> <EquationSource Format="TEX">\( \sqrt{-g}R \)</EquationSource> </InlineEquation> 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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月17日

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  • John Joseph M. Carrasco,
  • Suna Zekioğlu

摘要

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 − g R \( \sqrt{-g}R \) 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.