Phases of Dense Quarks at Large N_c

Abstract: In the limit of a large number of colors, N_c, we suggest that gauge theories can exhibit several distinct phases at nonzero temperature and quark density. Two are familiar: a cold, dilute phase of confined hadrons, where the pressure is ~ 1, and a hot phase of deconfined quarks and gluons, with pressure ~ N_c^2. When the quark chemical potential mu ~ 1, the deconfining transition temperature, T_d, is independent of mu. For T < T_d, as mu increases above the mass threshold, baryons quickly form a dense phase where the pressure is ~ N_c. As illustrated by a Skyrme crystal, chiral symmetry can be both spontaneously broken, and then restored, in the dense phase. While the pressure is ~ N_c, like that of (non-ideal) quarks, the dense phase is still confined, with interactions near the Fermi surface those of baryons, and not of quarks. Thus in the chirally symmetric region, baryons near the Fermi surface are parity doubled. We suggest possible implications for the phase diagram of QCD.

• The paper introduces a novel dense baryonic phase in QCD where pressure scales as N_c, marking a clear departure from conventional confined and deconfined phases.
• It employs the large N_c approximation to simplify complex QCD interactions, revealing distinct phase transitions under varying temperature and chemical potential.
• The study highlights potential experimental implications, including parity doubling from chiral symmetry restoration, which may inform heavy-ion and lattice QCD research.

Phases of Dense Quarks at Large $N_c$

The paper "Phases of Dense Quarks at Large $N_c$" by Larry McLerran and Robert D. Pisarski offers an advanced theoretical exploration of quark matter under extreme conditions, specifically within the framework of quantum chromodynamics (QCD) at a large number of colors, $N_c$. The authors investigate the phase structure at non-zero temperature and quark density, suggesting novel insights for QCD phase transitions and the corresponding implications.

The study commences by simplifying QCD to the large $N_c$ limit, a method postulated by 't Hooft as an insightful approximation for understanding non-perturbative aspects of QCD. In this limit, solving QCD becomes more tractable, revealing that different states and phases can emerge based on temperature and chemical potential variations.

Two well-known phases are discussed initially: a confined hadron phase, where pressure scales as $\sim 1$, and a deconfined, hot quark-gluon plasma, with pressure scaling as $\sim N_c^2$. Remarkably, the authors propose a third, dense baryonic phase, occurring when the quark chemical potential $\mu$ and temperature $T$ both satisfy $T < T_d$ and $\mu > 1$. This dense phase is characterized by pressure $\sim N_c$, aligning it more closely with that of baryons rather than free quarks.

A significant insight proposed is the idea that both confinement and chiral symmetry might exhibit intriguing behaviors in such dense quark matter. In particular, when quark densities rise beyond a certain point, baryons form a Fermi surface leading to a phenomenon where parity doubling appears as a consequence of chiral symmetry being restored in dense phases. Nonetheless, the phase remains confined, marking a stark departure from traditional perspectives that often tie chiral symmetry restoration to deconfinement.

The introduction of the Skyrme crystal model further highlights the complexity of QCD phases. Originally used to model nuclei as solitons, the Skyrme model's application to a dense baryonic phase indicates that chiral symmetry can be broken and then restored as density increases. This restoration admits parity doublets, a novel property not traditionally expected in dense quark matter.

The theoretical implications of this work are profound and suggest a reevaluation of the QCD phase diagram, with potential separation between deconfinement and chiral transitions at high density. Practically, while this theory primarily provides speculative insight, it hints at new phenomena that might be explored in heavy-ion collision experiments or using lattice QCD simulations—especially those probing the QCD critical point and transitions at non-zero baryon density.

Future developments could involve more detailed lattice simulations to verify the predicted behaviors of QCD at large $N_c$, particularly at densities and temperatures accessible in the quarkyonic phase regime. Such work may significantly deepen our understanding of strong interactions in extreme environments, akin to those found in neutron stars or during early universe conditions.

In essence, the paper enriches our theoretical understanding of QCD phases by leveraging the large $N_c$ limit, presenting challenging, yet potentially observable, QCD phenomena awaiting further confirmation and refinement.