Abstract :
We conjecture that the phase transitions in QCD at large number of colors image 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 image where θ-dependence of the vacuum energy experiences a sudden change in behavior: from image at image to image at image. This conjecture is also supported by recent lattice studies. We employ this conjecture to study a possible phase transition as a function of image from confinement to conformal phase in the Veneziano limit image 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 image the integral over instanton size is dominated by small-size instantons, making the instanton computations reliable with expected image behavior. However, when image, the integral over instanton size is dominated by large-size instantons, and the instanton expansion breaks down. This regime with image corresponds to the confinement phase. We also compute the variation of the critical image when the temperature and chemical potential image slightly vary. We also discuss the scaling image in the conformal phase.
