Massive Gravity from Double Copy

Abstract

We consider the double copy of massive Yang-Mills theory in four dimensions, whose decoupling limit is a nonlinear sigma model. The latter may be regarded as the leading terms in the low energy effective theory of a heavy Higgs model, in which the Higgs has been integrated out. The obtained double copy effective field theory contains a massive spin-2, massive spin-1 and a massive spin-0 field, and we construct explicitly its interacting Lagrangian up to fourth order in fields. We find that up to this order, the spin-2 self interactions match those of the dRGT massive gravity theory, and that all the interactions are consistent with a ${\Lambda }_3=(m^2{M}_{Pl}{)}^{1/3}$ cutoff. We construct explicitly the ${\Lambda }_3$ decoupling limit of this theory and show that it is equivalent to a bi-Galileon extension of the standard ${\Lambda }_3$ massive gravity decoupling limit theory. Although it is known that the double copy of a nonlinear sigma model is a special Galileon, the decoupling limit of massive Yang-Mills theory is a more general Galileon theory. This demonstrates that the decoupling limit and double copy procedures do not commute and we clarify why this is the case in terms of the scaling of their kinematic factors.

arXiv commentPublished version

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• On the Lagrangian formulation of the double copy to cubic order
• Towards Color-Kinematics Duality in Generic Spacetimes
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• Color-kinematics duality, double copy and the unitarity method for higher-derivative QCD and quadratic gravity
• Double-copy towards supergravity inflation with $\alpha$-attractor models
• Scattering Amplitudes of Kaluza-Klein Strings and Extended Massive Double-Copy
• Supersymmetric Massive Gravity
• Massive Color-Kinematics Duality and Double-Copy for Kaluza-Klein Scattering Amplitudes
• BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
• Topological Equivalence Theorem and Double-Copy for Chern-Simons Scattering Amplitudes
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• Cotton Double Copy for Gravitational Waves
• The seeds of EFT double copy