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 Nf ≪ 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 T = Tc where θ dependence experiences a sudden change in behavior. 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 > Tc, suddenly break down immediately below T < Tc 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 hot and dense QCD in large N limit by analyzing the θ dependence. We estimate the critical values for Tc and µc where the phase transition happens by approaching the critical values from the hot and/or dense regions where the instanton calculations are under complete theoretical control. We also describe some defects of various codimensions within a holographic model of QCD by focusing on their role around the phase transition point.