2017/10/31 by Andrew D. Bond, Daniel F. Litim, Gustavo Medina Vazquez +1 · 53 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Conformal map #Conformal symmetry #Cosmology #Cosmology and Gravitation Theories #Fixed point #Gauge theory #Geometry #Instability #Mathematical analysis #Mathematical physics #Mathematics #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Physics #Quantum Chromodynamics and Particle Interactions #Quantum electrodynamics #Quantum mechanics #Scaling #Theoretical physics #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.97.036019
published in Physical review. D/Physical review. D. 97(3) (American Physical Society) · 14 pages, 2 figures, 2 tables. v2: Added some discussion and references. New appendix with details of two-loop quartic calculations. Version accepted for publication in PRD
arxiv created 2018/01/24 · openalex publication_date 2018/02/20 · arxiv updated 2018/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.