UV conformal window for asymptotic safety

TL;DR

This paper investigates the conformal window in four-dimensional gauge theories using high-order perturbation theory, identifying conditions for asymptotic safety and stability, with implications for theoretical physics and cosmology.

Contribution

It provides a systematic perturbative analysis of fixed points and the conformal window in gauge theories up to NNLO, including stability and strong coupling considerations.

Findings

Determined the conformal window bounds using three-loop perturbation theory.

Identified fixed point mergers and vacuum instability as limits of the conformal window.

Suggested a possible secondary conformal window at strong coupling.

Abstract

Interacting fixed points in four-dimensional gauge theories coupled to matter are investigated using perturbation theory up to three loop order. It is shown how fixed points, scaling exponents, and anomalous dimensions are obtained as a systematic power series in a small parameter. The underlying ordering principle is explained and contrasted with conventional perturbation theory and Weyl consistency conditions. We then determine the conformal window with asymptotic safety from the complete next-to-next-to-leading order in perturbation theory. Limits for the conformal window arise due to fixed point mergers, the onset of strong coupling, or vacuum instability. A consistent picture is uncovered by comparing various levels of approximation. The theory remains perturbative in the entire conformal window, with vacuum stability dictating the tightest constraints. We also speculate about a secondary conformal window at strong coupling and estimate its lower limit. Implications for model building and cosmology are indicated.