Asymptotic safety guaranteed for strongly coupled gauge theories

We demonstrate that interacting ultraviolet fixed points in four dimensions exist at strong coupling and away from large-N Veneziano limits. This is established exemplarily for semisimple supersymmetric gauge theories with chiral matter and superpotential interactions by using the renormalization group and exact methods from supersymmetry. We determine the entire superconformal window of ultraviolet fixed points as a function of field multiplicities. Results are in accord with the a-theorem, bounds on conformal charges, Seiberg duality, and unitary. We also find manifolds of Leigh-Strassler models exhibiting lines of infrared fixed points. At weak coupling, findings are confirmed using perturbation theory up to three loop. Benchmark models with low field multiplicities are provided, including examples with Standard-Model-like gauge sectors. Implications for particle physics, model building, and conformal field theory are indicated.

Automated summary

We demonstrate the existence of interacting ultraviolet fixed points in four dimensions at strong coupling and away from large-N Veneziano limits. This is done using the renormalization group and exact methods from supersymmetry, exemplarily for semisimple supersymmetric gauge theories with chiral matter and superpotential interactions. We determine the entire superconformal window of ultraviolet fixed points and find manifolds of Leigh-Strassler models exhibiting lines of infrared fixed points. Perturbation theory up to three loop is used to confirm the findings at weak coupling, and benchmark models with low field multiplicities are provided. The implications for particle physics, model building, and conformal field theory are discussed.