BRST-Lagrangian Double Copy of Yang-Mills Theory

Abstract

We show that the double copy of gauge theory amplitudes to $\mathcal{N}=0$ supergravity amplitudes extends from tree level to loop level. We first explain that color-kinematic duality is a condition for the Becchi-Rouet-Stora-Tyutin operator and the action of a field theory with cubic interaction terms to double copy to a consistent gauge theory. We then apply this argument to Yang-Mills theory, where color-kinematic duality is known to be satisfied onshell at tree level. Finally, we show that the latter restriction can only lead to terms that can be absorbed in a sequence of field redefinitions, rendering the double copied action equivalent to $\mathcal{N}=0$ supergravity.

v2: 7 pages, improved presentation, published version

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• The Gauge Structure of Double Field Theory follows from Yang-Mills Theory
• Alternative formulations of the twistor double copy
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• The double copy of the multipole expansion
• Why is the Weyl double copy local in position space?
• Non-perturbative aspects of the self-dual double copy
• Geodesics From Classical Double Copy
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• Kinematic Hopf algebra for amplitudes and form factors
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• Tree-Level Color-Kinematics Duality Implies Loop-Level Color-Kinematics Duality up to Counterterms
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• Tree-Level Color-Kinematics Duality from Pure Spinor Actions
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• Towards an M5-Brane Model III: Self-Duality from Additional Trivial Fields
• Next-to-MHV Yang-Mills kinematic algebra
• The Weyl double copy from twistor space
• Massive Covariant Colour-Kinematics in 3D
• Out-of-time-order asymptotic observables are quasi-isomorphic to time-ordered amplitudes
• Algebraic Consistency and Explicit Construction of One-Loop BCJ Numerators of Yang-Mills and Related Theories
• Leading singularities in higher-derivative Yang-Mills theory and quadratic gravity
• The Kerr-Schild Double Copy in Lifshitz Spacetime
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