Double Copy from Homotopy Algebras

Abstract

We show that the BRST Lagrangian double copy construction of $\mathcal{N}=0$ supergravity as the `square' of Yang-Mills theory finds a natural interpretation in terms of homotopy algebras. We significantly expand on our previous work arguing the validity of the double copy at the loop level, and we give a detailed derivation of the double copied Lagrangian and BRST operator. Our constructions are very general and can be applied to a vast set of examples.

arXiv commentv2: 168 pages, presentation improved, typos fixed, published version

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• Off-Shell Color-Kinematics Duality for Chern-Simons
• Double Field Theory as the Double Copy of Yang-Mills
• Kinematic Lie Algebras From Twistor Spaces
• Asymptotic Weyl Double Copy
• Generalizations of the Double-Copy: the KLT Bootstrap
• Classical Spin Gravitational Compton Scattering
• Alternative formulations of the twistor double copy
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• Amplitudes, Hopf algebras and the colour-kinematics duality
• The double copy of the multipole expansion
• Superstring loop amplitudes from the field theory limit
• Why is the Weyl double copy local in position space?
• Geodesics From Classical Double Copy
• Non-perturbative aspects of the self-dual double copy
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• The single copy of the gravitational holonomy
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• Kinematic Hopf algebra for amplitudes and form factors
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• Braided Symmetries in Noncommutative Field Theory
• Double copy for Lagrangians at trilinear order
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