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The double copy formalism provides an intriguing connection between gauge theories and gravity. It was first demonstrated in the perturbative context of scattering amplitudes but recently the formalism has been applied to exact classical solutions in gauge theories such as the monopole and instanton. In this paper we will investigate how duality symmetries in the gauge theory double copy to gravity and relate these to solution generating transformations and the action of $Sl(2,R)$ in general relativity.
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We extend the perturbative classical double copy to the analysis of bound systems. We first obtain the leading order perturbative gluon radiation field sourced by a system of interacting color charges in arbitrary time dependent orbits, and test its validity by taking relativistic bremsstrahlung and non-relativistic bound state limits. By generalizing the color to kinematic replacement rules recently used in the context of classical bremsstrahlung, we map the gluon emission amplitude to the radiation fields of dilaton gravity sourced by interacting particles in generic (self-consistent) orbits. As an application, we reproduce the leading post-Newtonian radiation fields and energy flux for point masses in non-relativistic orbits from the double copy of gauge theory.
A characteristic value formulation of the Weyl double copy leads to an asymptotic formulation. We find that the Weyl double copy holds asymptotically in cases where the full solution is algebraically general, using rotating STU supergravity black holes as an example. The asymptotic formulation provides clues regarding the relation between asymptotic symmetries that follows from the double copy. Using the C-metric as an example, we show that a previous interpretation of this gravity solution as a superrotation has a single copy analogue relating the appropriate Lienard-Wiechert potential to a large gauge transformation.
We extend Shens recent formulation (arXiv:1806.07388) of the classical double copy, based on explicit color-kinematic duality, to the case of finite-size sources with non-zero spin. For the case of spinning Yang-Mills sources, the most general consistent double copy consists of gravitating objects which carry pairs of spin degrees of freedom. We find that the couplings of such objects to background fields match those of a classical (i.e. heavy) closed bosonic string, suggesting a string theory interpretation of sources related by color-kinematics duality. As a special case, we identify a limit, corresponding to unoriented strings, in which the 2-form Kalb-Ramond axion field decouples from the gravitational side of the double copy. Finally, we apply the classical double copy to extended objects, described by the addition of finite-size operators to the worldline effective theory. We find that consistency of the color-to-kinematics map requires that the Wilson coefficients of tidal operators obey certain relations, indicating that the extended gravitating objects generated by the double copy of Yang-Mills are not completely generic.
We consider the classical double copy, that relates solutions of biadjoint scalar, gauge and gravity theories. Using a recently developed twistor expression of this idea, we use well-established techniques to show that the multipole moments of arbitrary vacuum type D gravity fields are straightforwardly mapped to their counterparts in gauge and biadjoint scalar theory by the single and zeroth copies. We cross-check our results using previously obtained results for the Kerr metric. Our results provide further physical intuition of how the double copy operates.
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.
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