Confinement–deconfinement phase transition in hot and dense QCD at large N

Abstract

We conjecture that the confinement–deconfinement phase transition in QCD at large number of colors N and N f ≪ N at T ≠ 0 and μ ≠ 0 is triggered by the drastic change in θ behavior. The conjecture is motivated by the holographic model of QCD where confinement–deconfinement phase transition indeed happens precisely at the value of temperature T = T c where θ dependence experiences a sudden change in behavior [A. Parnachev, A. Zhitnitsky, arXiv: 0806.1736 [hep-ph]]. The conjecture is also supported by quantum field theory arguments when the instanton calculations (which trigger the θ dependence) are under complete theoretical control for T > T c , suddenly break down immediately below T < T c with sharp changes in the θ dependence. Finally, the conjecture is supported by a number of numerical lattice results. We employ this conjecture to study confinement–deconfinement phase transition of dense QCD at large μ in large N limit by analyzing the θ dependence. We find that the confinement–deconfinement phase transition at N f ≪ N happens at very large quark chemical potential μ c ∼ N Λ QCD . This result agrees with recent findings by McLerran and Pisarski [L. McLerran, R.D. Pisarski, Nucl. Phys. A 796 (2007) 83]. We also speculate on case when N f ∼ N .