  We give a theoretical framework to obtain a low-energy effective theory of
quantum chromodynamics (QCD) towards a first-principle derivation of
confinement/deconfinement and chiral-symmetry breaking/restoration crossover
transitions. In fact, we demonstrate that an effective theory obtained using
simple but non-trivial approximations within this framework enables us to treat
both transitions simultaneously on equal footing. A resulting effective theory
is regarded as a modified and improved version of nonlocal Polyakov-loop
extended Nambu-Jona-Lasinio (nonlocal PNJL) models proposed recently by Hell,
R\"ossner, Cristoforetti and Weise, and Sasaki, Friman and Redlich, extending
the original (local) PNJL model by Fukushima and others. A novel feature is
that the nonlocal NJL coupling depends explicitly on the temperature and
Polyakov loop, which affects the entanglement between confinement and chiral
symmetry breaking, together with the cross term introduced through the
covariant derivative in the quark sector considered in the conventional PNJL
model. The chiral symmetry breaking/restoration transition is controlled by the
nonlocal NJL interaction, while the confinement/deconfinement transition in the
pure gluon sector is specified by the nonperturbative effective potential for
the Polyakov loop obtained recently by Braun, Gies, Marhauser and Pawlowski.
The basic ingredients are a reformulation of QCD based on new variables and the
flow equation of the Wetterich type in the Wilsonian renormalization group.
This framework can be applied to investigate the QCD phase diagram at finite
temperature and density.
