Asymptotic Safety Guaranteed at Four Loop

TL;DR

This paper explores the existence and properties of four-dimensional quantum field theories with ultraviolet fixed points, providing detailed calculations up to four loops and insights into their phase structure and conformal window.

Contribution

It introduces the first four-loop gauge contributions to scalar beta functions in a specific class of gauge theories, advancing the understanding of asymptotic safety in 4d QFTs.

Findings

Identification of fixed points and scaling exponents up to three orders in the Veneziano parameter.

Analysis of the phase diagram and UV-IR trajectories contrasting with asymptotic freedom.

Insights into the conformal window, unitarity, and conformality loss mechanisms.

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 $\overline{\text{MS}}$ 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 non-trivial 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 4d non-supersymmetric conformal field theories with standard model-like field content, and invite further model building.