The double-copy method for supergravity amplitudes

Abstract: The double-copy construction enables the calculation of scattering amplitudes in theories of gravity by combining amplitudes from gauge theories. It relies on obtaining numerators that obey a duality between color and numerator factors, called color-kinematics duality. This construction is reviewed, along with the spinor-helicity formalism for onshell states and supersymmetry in amplitudes. Using generalized unitarity, a one-loop amplitude is verified from literature for a N = 2 theory obeying color-kinematics duality. This amplitude, along with a one-loop amplitude for a N = 0 theory are combined with the double copy in order to produce one-loop amplitudes from homogeneous supergravities. The one-loop divergence is studied with the methods of counterterm analysis, that is, operators necessary to cancel the on-shell matrix element of the divergence are identified for the amplitudes studied. It is interesting to note that all vectors produced from the double copy behave in the same way, that is, have the same divergence, for the four special cases of the magical supergravities. Furthermore, one of the counterterms vanishes for these four special cases, which is likely related to the enhanced symmetry that these theories posses.