Phase structure of anSU(N)gauge theory withNfflavors

We investigate the chiral phase transition in $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ gauge theories as the number of quark flavors, $N_f,$ is varied. We argue that the transition takes place at a large enough value of $N_f$ so that it is governed by the infrared fixed point of the β function. We study the nature of the phase transition analytically and numerically, and discuss the spectrum of the theory as the critical value of $N_f$ is approached in both the symmetric and broken phases. Since the transition is governed by a conformal fixed point, there are no light excitations on the symmetric side. We extend previous work to include higher order effects by developing a renormalization group estimate of the critical coupling.