  We investigate the interplay between lattice-symmetry breaking and
superconducting order in a two-dimensional model of doped antiferromagnets,
with long-range Coulomb interactions and Sp(2N) spin symmetry, in the large-N
limit. Our results motivate the outline of a global phase diagram for the
cuprate superconductors. We describe the quantum transitions between the
phases, the evolution of their fermion excitation spectrum, and the
experimental implications.
