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A percolation transition in Yang-Mills matter at finite number of colours

We examine baryonic matter at quark chemical potential of the order of the confinement scale, $μ_q\sim \lqcd$. In this regime, quarks are supposed to be confined but baryons are close to the ``tightly packed limit'' where they nearly overlap in configuration space. We show that this system will exhibit a percolation phase transition {\em when varied in the number of colours} $N_c$: at high $N_c$, large distance correlations at quark level are possible even if the quarks are essentially confined. At low $N_c$, this does not happen. We discuss the relevance of this for dense nuclear matter, and argue that our results suggest a new ``phase transition'', varying $N_c$ at constant $μ_q$.