Zero-temperature d-wave superconducting phase transition

The Ginzburg-Landau-Wilson theory that describes the disordered-metal-d-wave-superconductor phase transition at zero temperature is derived at weak coupling. The theory represents an interacting dissipative system of bosonic Cooper pairs in an effective random potential. I show that there exists a wide crossover regime in the theory controlled by a line of Gaussian fixed points, each of which in two dimensions is characterized by a different universal value of the de critical conductivity. Relation to experiments on overdoped and underdoped cuprates is discussed.