Pseudogap phase in the U(1) gauge theory with incoherent spinon pairs

The pseudogap effect of underdoped high-T-c superconductors is studied in t he U(1) gauge theory of the t-J model including the spinon pairing fluctuat ion. The gauge fluctuation breaks the long-range correlation between spinon pairs. The pairing fluctuation, however, suppresses significantly the low- lying gauge fluctuations and leads to a stable but phase incoherent spin-ga p phase, which is responsible for the pseudogap effects. The resistivity is suppressed by the phase fluctuation in this pseudogap phase, consistent wi th experiments.