  Proximity to a Mott insulating phase is likely to be an important physical
ingredient of a theory that aims to describe high-temperature superconductivity
in the cuprates. Quantum cluster methods are well suited to describe the Mott
phase. Hence, as a step towards a quantitative theory of the competition
between antiferromagnetism (AFM) and d-wave superconductivity (SC) in the
cuprates, we use Cellular Dynamical Mean Field Theory to compute zero
temperature properties of the two-dimensional square lattice Hubbard model. The
d-wave order parameter is found to scale like the superexchange coupling J for
on-site interaction U comparable to or larger than the bandwidth. The order
parameter also assumes a dome shape as a function of doping while, by contrast,
the gap in the single-particle density of states decreases monotonically with
increasing doping. In the presence of a finite second-neighbor hopping t', the
zero temperature phase diagram displays the electron-hole asymmetric
competition between antiferromagnetism and superconductivity that is observed
experimentally in the cuprates. Adding realistic third-neighbor hopping t''
improves the overall agreement with the experimental phase diagram. Since band
parameters can vary depending on the specific cuprate considered, the
sensitivity of the theoretical phase diagram to band parameters challenges the
commonly held assumption that the doping vs T_{c}/T_{c}^{max} phase diagram of
the cuprates is universal. The calculated ARPES spectrum displays the observed
electron-hole asymmetry. Our calculations reproduce important features of
d-wave superconductivity in the cuprates that would otherwise be considered
anomalous from the point of view of the standard BCS approach.
