Exploring infrared QCD with Schwinger-Dyson equations

The basic QCD building blocks are the Green's functions of the fundamental physical
degrees of freedom, gluons and quarks, and ghosts. Even though it is well-known that
these quantities are not physical, since they depend on the gauge-fixing scheme and
parameters used to quantize the theory, it is widely believed that QCD Green's functions
encode crucial information about the infrared dynamics of the theory. Due to the lattice
and Schwinger-Dyson communities focused efforts, we have now reached a point where
the interplay between these two non-perturbative tools can be fruitful. Several of the
above points will be reviewed in this talk, emphasizing the implications for the gluonic
and ghost sectors, the non-perturbative effective charge of QCD, and the chiral
symmetry breaking.