The phase diagram of the t-J model is investigated within the X-operator fo
rmalism using the Baym-Kadanoff theory and a 1/N expansion. In this way, no
auxiliary fields are introduced. For finite Coulomb repulsion, the system
shows a strong competition between d-wave superconductivity and d-wave flux
phase, leading to a strong suppression of superconductivity in the flux st
ate. The underdoped region is characterized by flux order in the normal sta
te, with a d-wave gap in the excitation spectrum, and by coexistence of bot
h superconductivity and flux phases below the superconducting transition te
mperature T-c. The balance between the two phases is determined by the shor
t-range Coulomb repulsion, while the long-range part of Coulomb interaction
prevents phase separation and leads to incommensurate charge-density-wave
state far away from the superconducting region.