Large $N_c$ QCD at non-zero chemical potential

Abstract

The general issue of large $N_c$ QCD at nonzero chemical potential is considered with a focus on understanding the difference between large $N_c$ QCD with an isospin chemical potential and large $N_c$ QCD with a baryon chemical potential. A simple diagrammatic analysis analogous to `t Hooft's analysis at $\mu =0$ implies that the free energy with a given baryon chemical potential is equal to the free energy with an isospin chemical potential of the same value plus $1/N_c$ corrections. Phenomenologically, these two systems behave quite differently. A scenario to explain this difference in light of the diagrammatic analysis is explored. This scenario is based on a phase transition associated with pion condensation when the isospin chemical potential exceeds $m_{\pi }/2$; associated with this transition there is breakdown of the $1/N_c$ expansion--in the pion condensed phase there is a distinct $1/N_c$ expansion including a larger set of diagrams. While this scenario is natural, there are a number of theoretical issues which at least superficially challenge it. Most of these can be accommodated. However, the behavior of quenched QCD which raises a number of apparently analogous issues cannot be easily understood completely in terms of an analogous scenario. Thus, the overall issue remains open.

References in corpus (2)

• Chiral symmetry breaking at large N_c
• Large Nc Continuum Reduction and the Thermodynamics of QCD

Cited by in corpus (11)

• Phases of Dense Quarks at Large N_c
• Thermodynamics of Two Flavor QCD to Sixth Order in Quark Chemical Potential
• Introductory lectures to large-N QCD phenomenology and lattice results
• Volume dependence of two-dimensional large-N QCD with a nonzero density of baryons
• Sign problem and phase quenching in finite-density QCD: models, holography, and lattice
• A NJL-based study of the QCD critical line
• Color Superconductivity at Large N: A New Hope
• Holographic realization of large-Nc orbifold equivalence with non-zero chemical potential
• QCD With A Chemical Potential, Topology, And The 't Hooft 1/N Expansion
• Silver Blaze Puzzle in 1/Nc Expansions of Cold and Dense QCD Matter
• Some exact results on the QCD critical point