  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.
