Conformal window in QCD for large numbers of colors and flavors

We conjecture that the phase transitions in QCD at large number of colors N≫1 is triggered by the drastic change in the instanton density. As a result of it, all physical observables also experience some sharp modification in the θ behavior. This conjecture is motivated by the holographic model of QCD where confinement-deconfinement phase transition indeed happens precisely at temperature T=Tc where θ-dependence of the vacuum energy experiences a sudden change in behavior: from N2cos⁡(θ/N) at TTc. This conjecture is also supported by recent lattice studies. We employ this conjecture to study a possible phase transition as a function of κ≡Nf/N from confinement to conformal phase in the Veneziano limit Nf∼N when number of flavors and colors are large, but the ratio κ is finite. Technically, we consider an operator which gets its expectation value solely from non-perturbative instanton effects. When κ exceeds some critical value κ>κc the integral over instanton size is dominated by small-size instantons, making the instanton computations reliable with expected exp⁡(−N) behavior. However, when κ<κc, the integral over instanton size is dominated by large-size instantons, and the instanton expansion breaks down. This regime with κ<κc corresponds to the confinement phase. We also compute the variation of the critical κc(T,μ) when the temperature and chemical potential T,μ≪ΛQCD slightly vary. We also discuss the scaling (xi−xj)−γdet in the conformal phase.