Abstract
We compute one-loop matter amplitudes in homogeneous Maxwell-Einstein supergravities with mathcal{N} = 2 supersymmetry using the double-copy construction. We start from amplitudes of mathcal{N} = 2 super-Yang-Mills theory with matter that obey 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 find a relation between the one-loop divergence of the supergravity amplitudes and the beta function of the non-supersymmetric gauge theory entering the construction. Two distinct linearized counterterms are generated at one loop. The divergence corresponding to the first is nonzero for all homogeneous supergravities, while the divergence associated to the second vanishes only in the case of the four Magical supergravities.
Highlights
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 find a relation between the one-loop divergence of the supergravity amplitudes and the beta function of the non-supersymmetric gauge theory entering the construction
In the case of gravitational theories that can be directly obtained from string theory, insight about color/kinematics duality can be obtained from string monodromy relations [43,44,45,46,47,48]
Supergravity amplitudes are constructed using as building blocks gauge-theory amplitudes between four hypermultiplets in a presentation that obeys color/kinematics duality
Summary
The left gauge theory entering the double-copy construction is a N = 2 sYM theory with a single half-hypermultiplet transforming in the same pseudo-real representation R which appears in the other gauge theory. This choice is motivated by the fact that a pseudoreal half-hypermultiplet is CPT self-conjugate and does not need to be augmented to a full hypermultiplet to have a sensible theory. There exists one infinite family of theories with symmetric scalar manifolds both in five and four dimensions, the so-called Generic Jordan family [67, 68] It has two distinct double-copy realizations, one with P = 0 and arbitrary D and the other with D = 6 and arbitrary P. We will discuss more in detail the UV properties of these theories .
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