Abstract
The double copy procedure relates gauge and gravity theories through color-kinematics replacements, and holds for both scattering amplitudes and in classical contexts. Moreover, it has been shown that there is a web of theories whose scattering amplitudes are related through operations that exchange color and kinematic factors. In this paper, we generalize and extend this procedure by showing that the classical perturbative double copy of pions corresponds to special Galileons. We consider point-particles coupled to the relevant scalar fields, and find the leading and next to leading order radiation amplitudes. By considering couplings motivated by those that would arise from extracting the longitudinal modes of the gauge and gravity theories, we are able to map the non-linear sigma model radiation to that of the special Galileon. We also construct the single copy by mapping the bi-adjoint scalar radiation to the non-linear sigma model radiation through generalized color-kinematics replacements.
Highlights
Time leads to the bi-adjoint scalar analogue, the zeroth copy
We assume that the special Galileon couples through a conformal transformation which is motivated by the coupling that would arise in the decoupling limit of massive gravity for the Galileons
We show that by applying a special set of color-kinematics replacements, it is possible to transform the radiation field generated by point-particles interacting through a bi-adjoint scalar field to the one in which these particles interact through a non-linear sigma model field
Summary
Time leads to the bi-adjoint scalar analogue, the zeroth copy. In the perturbative case, one can take the opposite direction and start from the bi-adjoint scalar, apply the corresponding replacements and obtain Yang-Mills theory, perform this one more time and obtain the gravitational theory. By considering a “dimensional reduction” of the gauge and gravity theories one can obtain the scattering amplitudes of the non-linear sigma model (NLSM) and the special Galileon, respectively [31, 32] The relation between these scalar theories and the gauge and gravity theories can be explained from another point of view: if we consider massive Yang-Mills and massive gravitational fields, the corresponding longitudinal modes are described by the non-linear sigma model and the (special1 [31, 33–35] ) Galileon respectively [36, 37]. This suggests the possibility of a broader relationship between these sets of theories.
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