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 $T=T_c$ where $\theta$ dependence experiences a sudden change in behavior. 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 hot and dense QCD in large $N$ limit by analyzing the $\theta$ dependence. We estimate the critical values for $T_c$ and $\mu_c$ 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.