Asymptotic safety guaranteed for strongly coupled gauge theories

TL;DR

This paper proves the existence of strongly coupled ultraviolet fixed points in four-dimensional gauge theories, expanding the understanding of asymptotic safety beyond large-N limits using supersymmetry and renormalisation group techniques.

Contribution

It demonstrates the existence of UV fixed points at strong coupling in four-dimensional gauge theories with supersymmetry, beyond large-N limits, and maps the superconformal window.

Findings

Existence of UV fixed points at strong coupling.

Agreement with the $a$-theorem and Seiberg duality.

Identification of models with Standard Model-like sectors.

Abstract

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 semi-simple supersymmetric gauge theories with chiral matter and superpotential interactions by using the renormalisation 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.