  We study the stability of the spin gap phase in the U(1) slave-boson theory
of the t-J model in connection to the underdoped cuprates. We approach the spin
gap phase from the superconducting state and consider the quantum phase
transition of the slave-bosons at zero temperature by introducing vortices in
the boson superfluid. At finite temperatures, the properties of the bosons are
different from those of the strange metal phase and lead to modified gauge
field fluctuations. As a result, the spin gap phase can be stabilized in the
quantum critical and quantum disordered regime of the boson system. We also
show that the regime of quantum disordered bosons with the paired fermions can
be regarded as the strong coupling version of the recently proposed nodal
liquid theory.
