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Lattice QCD with heavy quarks reduces to a three-dimensional effective theoryof Polyakov loops, which is amenable to series expansion methods. We analysethe effective theory in the cold and dense regime for a general number ofcolours, $N_c$. In particular, we investigate the transition from a hadron gasto baryon condensation. For any finite lattice spacing, we find the transitionto 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 differsfrom 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-likeand quark-like aspects. A lattice filling with baryon number shows a rapid andsmooth transition from condensing baryons to a crystal of saturated quarkmatter, due to the Pauli principle, and is consistent with this picture. Forcontinuum 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 rangeof lattice spacings and $N_c$-values, our results are stable when the limitsare approached in this order. We discuss possible implications for physicalQCD.

QCD in the heavy dense regime for general $N_c$: On the existence of quarkyonic matter