$ \mathcal{N} \geqslant {4} $ supergravity amplitudes from gauge theory at two loops

Abstract

We present the full two-loop four-graviton amplitudes in $ \mathcal{N} = 4,\;5,\;6 $ supergravity. These results were obtained using the double-copy structure of gravity, which follows from the recently conjectured color-kinematics duality in gauge theory. The two-loop four-gluon scattering amplitudes in $ \mathcal{N} = 0,\;{1},\;{2} $ supersymmetric gauge theory are a second essential ingredient. The gravity amplitudes have the expected infrared behavior: the two-loop divergences are given in terms of the squares of the corresponding one-loop amplitudes. The finite remainders are presented in a compact form. The finite remainder for $ \mathcal{N} = 8 $ supergravity is also presented, in a form that utilizes a pure function with a very simple symbol.