  Confirmation of the phononic origin of Cooper pair formation in
superconductors came with the demonstration that the interaction was retarded
and that the corresponding energy scales were associated with phonons. Using
cellular dynamical mean-field theory for the two-dimensional Hubbard model, we
identify such retardation effects in d-wave pairing and associate the
corresponding energy scales with short-range spin fluctuations. We find which
frequencies are relevant for pairing as a function of interaction strength and
doping and show that the disappearance of superconductivity on the overdoped
side coincides with the disappearance of the low energy feature in the
antiferromagnetic fluctuations, as observed in neutron scattering experiments.
