### Abstract

We construct all supergravity theories that can be obtained through factorized orbifold projections of N=8 supergravity, exposing their double-copy structure, and calculate their one-loop four-point scattering amplitudes. We observe a unified structure in both matter and gravity amplitudes, and demonstrate that the four-graviton amplitudes are insensitive to the precise nature of the matter couplings. We show that these amplitudes are identical for the two different realizations of N=4 supergravity with two vector multiplets, and argue that this feature extends to all multiplicities and loop orders as well as to higher dimensions. We also construct a selected set of supergravities obtained through a non-factorized orbifold action. Furthermore we calculate one-loop four-point amplitudes for all pure super-Yang-Mills theories with less-than-maximal supersymmetry using the duality between color and kinematics, finding here a unified expression that holds for all four gluon amplitudes in these theories. We recover the related amplitudes of factorized N ≤ 4 supergravities employing the double-copy construction. We observe a requirement that the four-point loop-level amplitudes have non-local integrand representations, exhibiting a mild non-locality in the form of inverse powers of the three external Mandelstam invariants. These are the first loop-level color-kinematic-satisfying representations in reduced supersymmetry theories.

Original language | English (US) |
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Article number | 56 |

Journal | Journal of High Energy Physics |

Volume | 2013 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 2013 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2013*(3), [56]. https://doi.org/10.1007/JHEP03(2013)056