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\ll N at T\neq 0 and \mu\neq 0 is triggered by the drastic change in \theta 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 \theta dependence experiences a sudden change in behavior[1]. The conjecture is also supported by quantum field theory arguments when the instanton calculations (which trigger the \theta dependence) are under complete theoretical control for T>T_c, suddenly break down immediately below T<T_c with sharp changes in the \theta 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 \mu in large N limit by analyzing the \theta dependence. We find that the confinement- deconfinement phase transition at N_f\ll N happens at very large quark chemical potential \mu_c\sim \sqrt{N}\Lambda_{QCD}. This result agrees with recent findings by McLerran and Pisarski[2]. We also speculate on case when N_f\sim N.