2008/08/31 by Oliver J. Rosten · 2 citations
Mathematics · Physics and Astronomy · #Abelian group #Asymptotic safety in quantum gravity #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Critical dimension #Dimension (graph theory) #Fixed point #Gauge theory #Geometry #Group (periodic table) #Infrared fixed point #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum #Quantum Chromodynamics and Particle Interactions #Quantum gravity #Quantum mechanics #Renormalization group #Scalar (mathematics) #Scalar field theory #Theoretical physics #Thermal quantum field theory #Triviality #Ultraviolet fixed point #Unitary state #cond-mat.other #hep-ph #hep-th
paper · pdf · doi:10.1088/1126-6708/2009/07/019
published as JHEP 0907:019,2009 · 14 pages, 6 figures; v2: Important addition - negative anomalous dimensions now treated; v3: error in treatment of negative anomalous dimension corrected and some clarifications added; v4: published in JHEP; very minor changes
openalex publication_date 2009/07/06 · arxiv created 2009/07/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Using the exact renormalization group, it is shown that no physically acceptable non-trivial fixed points, with positive anomalous dimension, exist for (i) O(N) scalar field theory in four or more dimensions, (ii) non-compact, pure Abelian gauge theory in any dimension. It is then shown, for both theories in any dimension, that otherwise physically acceptable non-trivial fixed points with negative anomalous dimension are non-unitary. In addition, a very simple demonstration is given, directly from the exact renormalization group, that should a critical fixed point exist for either theory in any dimension, then the n-point correlation functions exhibit the expected behaviour.