The nuclear liquid-gas phase transition at large $N_c$ in the Van der Waals approximation

We examine the nuclear liquid-gas phase transition at large number of colors ($N_c$) within the framework of the Van Der Waals (VdW) model. We argue that the VdW equation is appropriate at describing inter-nucleon forces, and discuss how each parameter scales with $N_c$. We demonstrate that $N_c=3$ (our world) is not large with respect to the other dimensionless scale relevant to baryonic matter, the number of neighbors in a dense system $N_N$. Consequently, we show that the liquid-gas phase transition looks dramatically different at $N_c \to \infty$ with respect of our world: The critical point temperature becomes of the order of $\lqcd$ rather than below it. The critical point density becomes of the order of the baryonic density, rather than an order of magnitude below it. These are precisely the characteristics usually associated with the "Quarkyonic phase". We therefore conjecture that quarkyonic matter is simply the large $N_c$ limit of the nuclear liquid, and the interplay between $N_c$ and $N_N$ is the reason why the nuclear liquid in our world is so different from quarkyonic matter. We conclude by suggesting ways our conjecture can be tested in future lattice measurements.