  Lattice QCD with heavy quarks reduces to a three-dimensional effective theory
of Polyakov loops, which is amenable to series expansion methods. We analyse
the effective theory in the cold and dense regime for a general number of
colours, $N_c$. In particular, we investigate the transition from a hadron gas
to baryon condensation. For any finite lattice spacing, we find the transition
to become stronger, i.e. ultimately first-order, as $N_c$ is made large.
Moreover, in the baryon condensed regime, we find the pressure to scale as
$p\sim N_c$ through three orders in the hopping expansion. Such a phase differs
from a hadron gas with $p\sim N_c^0$, or a quark gluon plasma, $p\sim N_c^2$,
and was termed quarkyonic in the literature, since it shows both baryon-like
and quark-like aspects. A lattice filling with baryon number shows a rapid and
smooth transition from condensing baryons to a crystal of saturated quark
matter, due to the Pauli principle, and is consistent with this picture. For
continuum physics, the continuum limit needs to be taken before the large $N_c$
limit, which is not yet possible in practice. However, in the controlled range
of lattice spacings and $N_c$-values, our results are stable when the limits
are approached in this order. We discuss possible implications for physical
QCD.
