  We study the fluctuations responsible for pairing in the $d$-wave
superconducting state of the two-dimensional Hubbard model at intermediate
coupling within a cluster dynamical mean-field theory with a numerically exact
quantum impurity solver. By analyzing how momentum and frequency dependent
fluctuations generate the $d-$wave superconducting state in different
representations, we identify antiferromagnetic fluctuations as the pairing glue
of superconductivity both in the underdoped and the overdoped regime.
Nevertheless, in the intermediate coupling regime, the predominant magnetic
fluctuations may differ significantly from those described by conventional
spin-fluctuation theory.
