Abstract
We give a double copy construction for the symmetries of the self-dual sectors of Yang-Mills (YM) and gravity, in the light-cone formulation. We find an infinite set of double copy constructible symmetries. We focus on two families which correspond to the residual diffeomorphisms on the gravitational side. For the first one, we find novel non-perturbative double copy rules in the bulk. The second family has a more striking structure, as a non-perturbative gravitational symmetry is obtained from a perturbatively defined symmetry on the YM side.At null infinity, we find the YM origin of the subset of extended Bondi-Metzner-Sachs (BMS) symmetries that preserve the self-duality condition. In particular, holomorphic large gauge YM symmetries are double copied to holomorphic supertranslations. We also identify the single copy of superrotations with certain non-gauge YM transformations that to our knowledge have not been previously presented in the literature.
Highlights
The idea of gravity as a double copy (DC)1 has found applications in the study of numerous aspects of the gravitational theory, most notably scattering amplitudes, where much of the recent success has been driven by the identification of a duality between the color and kinematic factors, the so-called Bern-Carrasco-Johannson (BCJ) duality [4,5,6,7,8,9,10,11]
We focus on two families which correspond to the residual diffeomorphisms on the gravitational side
Having understood how the first family of gravitational symmetries can be obtained from the YM ones, we focus on the second family of gravitational symmetries: δcφ
Summary
The idea of gravity as a double copy (DC) has found applications in the study of numerous aspects of the gravitational theory, most notably scattering amplitudes, where much of the recent success has been driven by the identification of a duality between the color and kinematic factors, the so-called Bern-Carrasco-Johannson (BCJ) duality [4,5,6,7,8,9,10,11]. Having a DC prescription for the local symmetries of the fields (i.e. the gauge transformations on the Yang-Mills (YM) side and diffeomorphisms on the gravity side) is a proof of the robustness of the DC dictionaries for the fields, but the possible applications of such a prescription go beyond this It was shown in [40, 44, 58], working in the BRST formalism, that one can exploit it to obtain a gauge-mapping algorithm, which gives a gravity gauge fixing functional output from a YM gauge-fixing functional input. We find that the repackaging described above recasts the gravity transformation as a perturbative non-local series This is obtainable from its YM counterpart via the same simple rules as the first family, verifying the robustness of our construction. The first family maps holomorphic YM large gauge symmetries to holomorphic supertranslations, whereas the second one identifies certain (non-gauge and non-local) SDYM transformations to holomorphic superrotations..
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