Asymptotic safety guaranteed at four-loop order
Daniel F. Litim, Nahzaan Riyaz, Emmanuel Stamou, Tom Steudtner
Abstract
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 $\overline{\mathrm{MS}}$ scheme for a template $SU({N}_{c})$ gauge theory coupled to ${N}_{f}$ 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.