Gauge invariant double copy of Yang-Mills theory: the quartic theory

Abstract

We give an explicit gauge invariant, off-shell and local double copy construction of gravity from Yang-Mills theory to quartic order. To this end we use the framework of homotopy algebras, and we identify a rich new algebraic structure associated to color-stripped Yang-Mills theory. This algebra, which is a generalization of a Batalin-Vilkovisky algebra, is the underlying structure necessary for double copy. We give a self-contained introduction into these algebras by illustrating them for Chern-Simons theory in three dimensions. We then construct N = 0 supergravity in the form of double field theory in terms of the algebraic Yang-Mills building blocks to quartic order in interactions. As applications of the same universal formula, we re-derive the 4-graviton scattering amplitude and compute a chiral form of the Courant algebroid gauge structure of double field theory.

30 pages plus appendix and references. Published version

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• New Relations for Gauge-Theory Amplitudes
• Double Field Theory
• Black holes and the double copy
• The gauge algebra of double field theory and Courant brackets
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• The Kinematic Algebra From the Self-Dual Sector
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Cited by in corpus (8)

• Scattering Amplitudes in Quantum Field Theory
• Gauge independent kinematic algebra of self-dual Yang-Mills theory
• Double-Copying Self-Dual Yang-Mills Theory to Self-Dual Gravity on Twistor Space
• Double Copy from Tensor Products of Metric BV${}^{■}$-algebras
• Tree-Level Color-Kinematics Duality from Pure Spinor Actions
• Out-of-time-order asymptotic observables are quasi-isomorphic to time-ordered amplitudes
• Ambitwistor Yang-Mills Theory Revisited
• The Dark Side of Double-Tensor Multiplets