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 $p\sim N_c$ through three orders in the hopping expansion. Such a phase differs from a hadron gas with $p\sim N_c^0$, or a quark gluon plasma, $p\sim N_c^2$, 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.

arXiv comment24 pages, 7 figures; one figure and one reference added, reworded abstract and conclusions, version accepted for publication

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• Holographic approach to compact stars and their binary mergers
• Chiral spin symmetry and the QCD phase diagram
• Pion spectral properties above the chiral crossover of QCD
• Neutron stars and phase diagram in a hard-wall AdS/QCD model
• Heavy Holographic QCD
• Might Normal Nuclear Matter be Quarkyonic?
• The fate of the critical endpoint at large $N_c$
• Color-flavor dependence of the Nambu-Jona-Lasinio model and QCD phase diagram
• The Polyakov loop models in the large N limit: Phase diagram at finite density
• Strong coupling methods in QCD thermodynamics
• Correlations between nuclear incompressibility, liquid-gas critical point, and quarkyonic transition
• QCD at high temperature and density: selected highlights