2016/05/31 by I. Hamzaan Bridle, Tim R. Morris · 23 citations
Mathematics · Physics and Astronomy · #Applied mathematics #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Cutoff #Effective action #Fixed point #Functional renormalization group #Gaussian #Legendre polynomials #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Renormalization #Renormalization group #Scalar (mathematics) #Scalar field #Scalar field theory #Statistical physics #Universality (dynamical systems) #cond-mat.stat-mech #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.94.065040
published in Physical review. D/Physical review. D. 94(6) (American Physical Society) · 32 pages, 1 figure; extended to exact treatment
arxiv created 2016/07/12 · openalex publication_date 2016/09/28 · arxiv updated 2016/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present an exact renormalization group (RG) analysis of O(N)-invariant scalar field theory about the Gaussian fixed point. We prove a series of statements that, taken together, show that the nonpolynomial eigenperturbations found in the local potential approximation at the linearized level do not lead to new interactions, i.e. enlarge the universality class, in the local potential approximation nor treated exactly. Nonperturbatively, their RG flow does not emanate from the fixed point. For the equivalent Wilsonian effective action, they can be reexpressed in terms of the usual couplings to polynomial interactions, which can furthermore be tuned to be as small as desired for all finite RG time. For the infrared cutoff Legendre effective action, this can also be done for the infrared evolution. We explain why this is nevertheless consistent with the fact that the large field behavior is fixed by these perturbations.