Curvature-squared multiplets, evanescent effects, and the U(1) anomaly in N=4 supergravity

We evaluate one-loop amplitudes of N=4 supergravity in D dimensions using the double-copy procedure that expresses gravity integrands in terms of corresponding ones in Yang--Mills theory. We organize the calculation in terms of a set of gauge-invariant tensors, allowing us to identify evanescent contributions. Among the latter, we find the matrix elements of supersymmetric completions of curvature-squared operators. In addition, we find that such evanescent terms and the U(1)-anomalous contributions to one-loop N=4 amplitudes are tightly intertwined. The appearance of evanescent operators in N=4 supergravity and their relation to anomalies raises the question of their effect on the known four-loop divergence in this theory. We provide bases of gauge-invariant tensors and corresponding projectors useful for Yang--Mills theories as a by-product of our analysis.