Asymptotic safety guaranteed at four-loop order

We investigate a family of four-dimensional quantum field theories with weakly interacting ultraviolet fixed points up to four-loop order in perturbation theory. Key new ingredients are the three-loop gauge contributions to quartic scalar beta functions, which we compute in the MS̄ scheme for a template SU(Nc) gauge theory coupled to Nf fundamental fermions and elementary scalars. We then determine fixed point couplings, field and mass anomalous dimensions, and universal scaling exponents up to the first three nontrivial orders in a small Veneziano parameter. The phase diagram and UV-IR connecting trajectories are found and contrasted with asymptotic freedom. Further, the size of the conformal window, unitarity, and mechanisms leading to the loss of conformality are investigated. Our results provide blueprints for concrete four-dimensional nonsupersymmetric conformal field theories with standard model-like field content and invite further model building.