  Using the U(1) holon pair slave boson theory [Phys. Rev. B 64, 052501 2001)],
we derive a low energy field theory of dealing with both d-wave
superconductivity and antiferromagnetism for underdoped cuprates by
constructing both the Cooper pair field and the chargon pair field. In terms of
the internal gauge field, the Cooper pair field carries no internal charge
while the chargon pair field carries the internal charge. They are decoupled in
the low energy limit. This allows us to separately treat the XY model of the
Cooper pair field to describe superconductivity and the Abelian Higgs model of
the chargon pair field to describe antiferromagnetism in the presence of Dirac
fermions at and near the d-wave nodal points. Thus we find that the d-wave
superconductivity can coexist with antiferromagnetism and that despite the
coexistence, the antiferromagnetism can not affect the superconducting
transition, thus allowing the XY universality class in the extreme type II
limit.
