QCD in the heavy dense regime for general N c : on the existence of quarkyonic matter

Abstract

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 ∼ N_c through three orders in the hopping expansion. Such a phase differs from a hadron gas with p ∼Nc0\[ {N}_c^0 \], or a quark gluon plasma, p ∼Nc2\[ {N}_c^2 \], 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.