One-loop Amplitudes for N = 2 Homogeneous Supergravities
Authors: Maor Ben-Shahar and Marco Chiodaroli
Preprint number: UUITP-57/18
In this paper, we compute one-loop matter amplitudes in homogeneous Maxwell-Einstein supergravities with N = 2 supersymmetry in four dimensions using a double-copy construction which was established in arXiv:1512.09130. We start from a presentation of amplitudes in a super-Yang-Mills theory with matter hypermultiplet which obeys manifestly the duality between color and kinematics. Taking advantage of the fact that amplitudes with external hypermultiplets have kinematical numerators which do not present any explicit dependence on the loop momentum, we are able to find a relation between the one-loop divergence of the supergravity amplitudes and the beta function of the non-supersymmetric gauge theory entering the double-copy construction. We find that two distinct counterterms are generated at one loop. The divergence corresponding to the first is nonzero for all homogeneous supergravities. The divergence associated to the second vanishes only in the case of the four Magical supergravities.