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We examine the interplay between the percolation and the deconfinement phasetransitions of Yang-Mills matter at finite temperature, quark chemicalpotential $\mu_Q$ and number of colors $N_c$. We find that, whereas thecritical $N_c$ for percolation goes down with density, the critical $N_c$ forconfinement generally goes up. Because of this, Yang-Mills matter falls intotwo qualitatively different regimes: the "low-$N_c$ limit", where percolationdoes not occur because matter deconfines before it percolates, and thehigh-$N_c$ limit, where there are three distinct phases characterizingYang-Mills matter at finite temperature and density: confined, deconfined andconfined but percolating matter. The latter can be thought of as the recentlyconjectured "quarkyonic phase". We attempt to estimate the critical $N_c$, tosee if the percolating phase can occur in our world. We find that, whilepercolation will not occur at normal nuclear density as in the large-$N_c$limit, a sliver of the phase diagram in $N_c$, energy density and baryonicdensity where percolation occurs while confinement persists is possible. Weconclude by speculating on the phenomenological properties of such percolating"quarkyonic" matter, suggest avenues to study it quantitatively, and look forit in experiment.

Quarkyonic Percolation and deconfinement at finite density and number of colors