One-loop four-point amplitudes in pure and matter-coupled N <= 4 supergravity

TL;DR

This paper constructs and analyzes one-loop four-point amplitudes in various supergravity and super-Yang-Mills theories, revealing a unified structure, insensitivity to matter couplings, and introducing non-local integrand representations.

Contribution

It provides a comprehensive construction of supergravity theories via orbifold projections, calculates their one-loop amplitudes, and introduces non-local integrand representations satisfying color-kinematics duality.

Findings

Four-graviton amplitudes are insensitive to matter couplings.

Unified expression for all four-gluon amplitudes in less-than-maximal super-Yang-Mills.

First loop-level color-kinematic-satisfying representations in reduced supersymmetry theories.

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 the 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.