  Within the two-dimensional repulsive t-t'-Hubbard model, an attractive
coupling in the d-wave pairing channel is induced by antiferromagnetic
fluctuations. We investigate this coupling using functional renormalization
group equations. The momentum dependent d-wave coupling can be bosonized by the
use of scale dependent field transformations. We propose an effective coarse
grained model for the Hubbard model which is based on the exchange of
antiferromagnetic and d-wave collective bosons.
