  Based on the three-flavor Polyakov-looped Nambu$-$Jona-Lasinio (pNJL) model,
we have studied the structure of the three-dimensional QCD phase diagram with
respect to the temperature, the baryon chemical potential, and the isospin
chemical potential, by investigating the interplay among the chiral quark
condensate, the pion condensate, and the Polyakov loop. While the pNJL model
leads to qualitatively similar structure of the normal quark phase, the pion
superfluid phase, and the Sarma phase as well as their phase boundaries, when
compared to the NJL model, the inclusion of the Polyakov loop enlarges
considerably the areas of the pion superfluid phase and the Sarma phase, and
leads to critical end points at higher temperatures. With the contribution of
the gluon dynamics effectively included, the present study is expected to give
a more reliable prediction of the three-dimensional QCD phase diagram compared
to that in the NJL model.
