Two-loop n-point anomalous amplitudes in N =4 supergravity

Abstract

We compute the anomalous two-loop four-point amplitudes in N =4 pure supergravity, using unitarity and the double-copy construction. We also present all terms determined by four-dimensional cuts in two all-multiplicity two-loop anomalous superamplitudes. This result provides the first twoloop n-point gravity amplitude, up to a class of undetermined terms, which we determine completely at four points.We show that a recently proposed finite counterterm cancels these amplitudes to this order. We argue that the counterterm does not spoil the three-loop finiteness of anomalous amplitudes in the N =4 theory.