Conformal windows beyond asymptotic freedom

We study four-dimensional gauge theories coupled to fermions in the fundamental and mesonlike scalars. All requisite beta functions are provided for general group fermion representation. In regime where asymptotic freedom is absent, we determine all interacting fixed points using perturbation theory up three loop two Yukawa quartic couplings. find that conformal window of ultraviolet narrowed down by finite-$N$ corrections beyond Veneziano limit. also a new infrared point whose main features, such as scaling exponents, UV-IR connecting trajectories, phase diagram, provided. Both collide upon varying number flavors ${N}_{\mathrm{f}}$, conformality lost through saddle-node bifurcation. further revisit prospect large-${N}_{\mathrm{f}}$ limit matter field fluctuations dominate. Unlike at weak coupling, do not clear evidence solutions even presence scalar