Superconducting Transition in Doped Antiferromagnet

We investigate the superconducting transition in a doped antiferromagnet. Based on the phase string framework of the t-J model, an effective model describing the phase-coherence transition is obtained and is studied through duality transformation and renormalization group treatment . We show that such a topological transition is controlled by spin excitations, with the transition temperature determined by a characterisitic spin excitation energy. The existence of an Ising-like long range order of staggered current loops is also discussed.