Triviality from the Exact Renormalization Group

Abstract

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.

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

References in corpus (30)

• Exact Renormalization Group Equations. An Introductory Review
• Renormalisation of ϕ^4-theory on noncommutative R^4 in the matrix base
• Perfect lattice action for asymptotically free theories
• Derivative Expansion of the Exact Renormalization Group
• Elements of the Continuous Renormalization Group
• On Truncations of the Exact Renormalization Group
• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• Scheme Independence and the Exact Renormalization Group
• A gauge invariant exact renormalization group I
• Three dimensional massive scalar field theory and the derivative expansion of the renormalization group
• Exact Scheme Independence
• Rapidly Converging Truncation Scheme of the Exact Renormalization Group
• A Generalised Manifestly Gauge Invariant Exact Renormalisation Group for SU(N) Yang-Mills
• On the Fixed-Point Structure of Scalar Fields
• Non-Trivial Directions for Scalar Fields
• A Manifestly Gauge Invariant, Continuum Calculation of the SU(N) Yang-Mills two-loop beta function
• Manifestly Gauge Invariant QCD
• A proposal for a manifestly gauge invariant and universal calculus in Yang-Mills theory
• Exact scheme independence at two loops
• Exact scheme independence at one loop
• Non-Compact Pure Gauge QED in 3D is Free
• Manifestly gauge invariant QED
• A manifestly gauge invariant exact renormalization group
• A Manifestly Gauge Invariant and Universal Calculus for SU(N) Yang-Mills
• General Computations Without Fixing the Gauge
• Universality From Very General Nonperturbative Flow Equations in QCD
• A Primer for Manifestly Gauge Invariant Computations in SU(N) Yang-Mills
• A Resummable beta-Function for Massless QED
• Unitarity Bound of the Wave Function Renormalization Constant
• Constraints on an Asymptotic Safety Scenario for the Wess-Zumino Model

Cited by in corpus (20)

• Fundamentals of the Exact Renormalization Group
• Asymptotic safety guaranteed
• Bootstrapping Mixed Correlators in the Five Dimensional Critical O(N) Models
• Critical behavior in spherical and hyperbolic spaces
• Higgs Mass Bounds from Renormalization Flow for a Higgs-top-bottom model
• Higgs Mass Bounds from Renormalization Flow for a simple Yukawa model
• Asymptotically free scaling solutions in nonabelian Higgs models
• Nonabelian Higgs models: paving the way for asymptotic freedom
• Interacting Scalar Fields in the Context of Effective Quantum Gravity
• On the Question of an Ultraviolet Zero of the Beta Function of the $\lambda ({\vec{\varphi }}^2{)}_4^2$ Theory
• More on the cubic versus quartic interaction equivalence in the $O(N)$ model
• On the Renormalization of Theories of a Scalar Chiral Superfield
• Equivalent Fixed-Points in the Effective Average Action Formalism
• Stability of fixed points and generalized critical behavior in multifield models
• New Renormalization Group Equations and the Naturalness Problem
• An Extension of Pohlmeyer's Theorem
• Fate of the scalar quartic couplings in the inert models
• An asymptotic-safety mechanism for chiral Yukawa systems
• A Information-Theoretic View on Spacetime
• Functional truncations in asymptotic safety for quantum gravity