  Our understanding of the dynamics and the phase structure of dense
strong-interaction matter is to a large extent still built on the analysis of
low-energy models, such as those of the Nambu-Jona-Lasinio-type. In this work,
we analyze the emergence of the latter class of models at intermediate and low
energy scales from fundamental quark-gluon interactions. To this end, we study
the renormalization group flow of a Fierz-complete set of four-quark
interactions and monitor their strength at finite temperature and quark
chemical potential. At small quark chemical potential, we find that the
scalar-pseudoscalar interaction channel is dynamically rendered most dominant
by the gauge degrees of freedom, indicating the formation of a chiral
condensate. Moreover, the inclusion of quark-gluon interactions leaves a
significant imprint on the dynamics as measured by the curvature of the
finite-temperature phase boundary which we find to be in accordance with
lattice QCD results. At large quark chemical potential, we then observe that
the dominance pattern of the four-quark couplings is changed by the underlying
quark-gluon dynamics, without any fine-tuning of the four-quark couplings. In
this regime, the scalar-pseudoscalar interaction channel becomes subleading and
the dominance pattern suggests the formation of a chirally symmetric diquark
condensate. In particular, our study confirms the importance of explicit
$U_{\mathrm{A}}(1)$ breaking for the formation of this type of condensate at
high densities.
