  N=4 Poincare supergravity has a global SU(1,1) duality symmetry that acts
manifestly only on shell as it involves duality rotations of vector fields. A
U(1) subgroup of this symmetry is known to be anomalous at the quantum level in
the presence of a non-trivial gravitational background. We first derive this
anomaly from a novel perspective, by relating it to a similar anomaly in
conformal supergravity where SU(1,1) acts off shell, using the fact that N=4
Poincare supergravity has a superconformal formulation. We explicitly construct
the corresponding local and nonlocal anomalous terms in the one-loop effective
action. We then study how this anomaly is reflected in the supergravity
S-matrix. Calculating one-loop N=4 supergravity scattering amplitudes (with and
without additional matter multiplets) using color/kinematics duality and the
double-copy construction we find that a particular U(1) symmetry which was
present in the tree-level amplitudes is broken at the quantum level. This
breaking manifests itself in the appearance of new one-loop N=4 supergravity
amplitudes that have non-vanishing soft-scalar limits (these amplitudes are
absent in N>4 supergravities). We discuss the relation between these
symmetry-violating amplitudes and the corresponding U(1) anomalous term in the
one-loop supergravity effective action.
