## Conformal window in QCD for large numbers of colours and flavours    [PDF]

Ariel R. Zhitnitsky
We conjecture that the phase transitions in QCD at large number of colours $N\gg 1$ is triggered by the drastic change in $\theta$ behaviour. The conjecture is motivated by the holographic model of QCD where confinement -deconfinement phase transition indeed happens precisely at temperature $T=T_c$ where $\theta$ dependence experiences a sudden change in behaviour: from $N^2\cos(\theta/N)$ at $TT_c$. This conjecture is also supported by recent lattice studies. We employ this conjecture to study a possible phase transition as a function of $\kappa\equiv N_f/N$ from confinement to conformal phase in the Veneziano limit $N_f\sim N$ when number of flavours and colours are large, but the ratio $\kappa$ is finite. Technically, we consider an operator which gets its expectation value solely from nonperturbative instaton effects. When $\kappa$ exceeds some critical value $\kappa> \kappa_c$ the integral over instanton size is dominated by small-size instatons, making the instanton computations reliable with expected $\exp(-N)$ behaviour. However, when $\kappa<\kappa_c$, the integral over instaton size is dominated by large-size instantons, and the instanton expansion breaks down. This regime with $\kappa<\kappa_c$ corresponds to the confinement phase. We also compute the variation of the critical $\kappa_c(T, \mu)$ when the temperature and chemical potential $T, \mu \ll \Lambda_{QCD}$ slightly vary. We also discuss the scaling $(x_i-x_j)^{-\gamma_{\rm det}}$ in the conformal phase.
View original: http://arxiv.org/abs/1308.0020