Reexamination of d-wave superconductivity in the two-dimensional Hubbard   model
  We reexamine the possibility of d-wave superconductivity in the hole-doped two-dimensional Hubbard model. In terms of the gauge field description of the spin fluctuations, we show that d-wave superconductivity is unstable in the perturbative region with respect to the on-site Coulomb repulsion, U. Whereas in the region where d-wave superconductivity is possible, there is a strong constraint on the gap of superconductivity. Analysis of the localized spin moments suggests that there is another d-wave (d_{x^2-y^2}-wave) pairing due to the short-range antiferromagnetic correlation. 
Takao Morinari