QCD in the heavy dense regime for general Nc: 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, Nc. 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 Nc is made large. Moreover, in the baryon condensed regime, we find the pressure to scale as p ∼ Nc through three orders in the hopping expansion. Such a phase differs from a hadron gas with p ∼ {N}_c^0 , or a quark gluon plasma, p ∼ {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 Nc limit, which is not yet possible in practice. However, in the controlled range of lattice spacings and Nc-values, our results are stable when the limits are approached in this order. We discuss possible implications for physical QCD.