  We study the effect of dynamical Holstein phonons on the physics of the
Hubbard model at small doping using the dynamical cluster approximation on a
$2\times2$ cluster. Non-local antiferromagnetic correlations are found to
significantly enhance the electron-phonon coupling, resulting in polaron
formation for moderate coupling strengths. At finite doping, the
electron-phonon coupling is found to strongly enhance the non-local spin
correlations, indicating a synergistic interplay between the electron-phonon
coupling and antiferromagnetic correlations. Although it enhances the pairing
interaction, the electron-phonon coupling is found to decrease the
superconducting transition temperature, due to the reduction in the
quasiparticle fraction.
