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Register a new userDouble Copy Relation for AdS
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Xinan Zhou
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We present a double copy relation in AdS$_5$ which relates tree-level four-point amplitudes of supergravity, super Yang-Mills and bi-adjoint scalars.
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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 present a novel double-copy prescription for gauge fields at the Lagrangian level and apply it both to the original double copy and the soft theorem. The Yang-Mills Lagrangian in light-cone gauge is mapped directly to the $mathcal{N}=0$ supergravity Lagrangian in light-cone gauge to trilinear order, and we show that the obtained result is manifestly equivalent to Einstein gravity at tree level up to this order. The application of the double-copy prescription to the soft-collinear effective QCD Lagrangian yields an effective description of an energetic Dirac fermion coupled to the graviton, Kalb-Ramond, and dilaton fields, from which the fermionic gravitational soft and next-to-soft theorems follow.
We establish the status of the Weyl double copy relation for radiative solutions of the vacuum Einstein equations. We show that all type N vacuum solutions, which describe the radiation region of isolated gravitational systems with appropriate fall-off for the matter fields, admit a degenerate Maxwell field that squares to give the Weyl tensor. The converse statement also holds, i.e. if there exists a degenerate Maxwell field on a curved background, then the background is type N. This relation defines a scalar that satisfies the wave equation on the background. We show that for non-twisting radiative solutions, the Maxwell field and the scalar also satisfy the Maxwell equation and the wave equation on Minkowski spacetime. Hence, non-twisting solutions have a straightforward double copy interpretation.
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.
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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