  In the $t-J$ model, the electron fractionalization is unique due to the
non-perturbative phase string effect. We formulated a lattice field theory
taking this effect into full account. Basing on this field theory, we
introduced a pair of Wilson loops which constitute a complete set of order
parameters determining the phase diagram in the underdoped regime. We also
established a general composition rule for electric transport expressing the
electric conductivity in terms of the spinon and the holon conductivities. The
general theory is applied to studies of the quantum phase diagram. We found
that the antiferromagnetic and the superconducting phases are dual: in the
former, holons are confined while spinons are deconfined, and {\it vice versa}
in the latter. These two phases are separated by a novel phase, the so-called
Bose-insulating phase, where both holons and spinons are deconfined and the
system is electrically insulating.

Strongly Correlated Electrons;Superconductivity