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We investigate QCD with a large number of massless flavors with the aid ofrenormalization group flow equations. We determine the critical number offlavors separating the phases with and without chiral symmetry breaking inSU(Nc) gauge theory with many fermion flavors. Our analysis includes allpossible fermionic interaction channels in the pointlike four-fermion limit.Constraints from gauge invariance are resolved explicitly and regulator-schemedependencies are studied. Our findings confirm the existence of an Nf windowwhere the system is asymptotically free in the ultraviolet, but remainsmassless and chirally invariant on all scales, approaching a conformal fixedpoint in the infrared. Our prediction for the critical number of flavors of thezero-temperature chiral phase transition in SU(3) is Nf^{cr}=10.0\pm  0.29(fermion)[+1.55;-0.63](gluon), with the errors arising fromapproximations in the fermionic and gluonic sectors, respectively.Comment: 7 pages, 3 figures, updated discussion of the uncertainties in the  gauge secto

Chiral phase structure of QCD with many flavors