Topological Gauge Structure and Phase Diagram for Weakly Doped Antiferromagnets

We show that the topological gauge structure in the phase string theory of the {\rm t-J} model gives rise to a global phase diagram of antiferromagnetic (AF) and superconducting (SC) phases in a weakly doped regime. Dual confinement and deconfinement of holons and spinons play essential roles here, with a quantum critical point at a doping concentration $x_c\simeq 0.043$. The complex experimental phase diagram at low doping is well described within such a framework.Comment: 4 pages, 2 figures, modified version, to appear in Phys. Rev. Let