UV and IR Zeros of Gauge Theories at The Four Loop Order and Beyond

Abstract

We unveil the general features of the phase diagram for any gauge theory with fermions transforming according to distinct representations of the underlying gauge group, at the four-loop order. We classify and analyze the zeros of the perturbative beta function and discover the existence of a rich phase diagram. The anomalous dimension of the fermion masses, at the infrared stable fixed point, are presented. We show that the infrared fixed point, and associated anomalous dimension, are well described by the all-orders beta function for any theory. We also argue the possible existence, to all orders, of a nontrivial ultraviolet fixed point for gauge theories at large number of flavors.

Minor corrections, main results unchanged. RevTeX, 9 pages, 6 figures

References in corpus (13)

• Supersymmetry Inspired QCD Beta Function
• Zero of the discrete beta function in SU(3) lattice gauge theory with color sextet fermions
• The physics of eight flavours
• Nearly conformal gauge theories in finite volume
• The infrared dynamics of Minimal Walking Technicolor
• Spectrum of SU(2) lattice gauge theory with two adjoint Dirac flavours
• Phase structure of SU(3) gauge theory with two flavors of symmetric-representation fermions
• Large N flavor beta-functions: a recap
• Higher representations on the lattice: perturbative studies
• Hot Conformal Gauge Theories
• Magnetic S-parameter
• Orthogonal Technicolor with Isotriplet Dark Matter on the Lattice
• QCD Dual

Cited by in corpus (103)

• Renormalisation group and the Planck scale
• Lattice tests of beyond Standard Model dynamics
• Nonperturbative investigations of SU(3) gauge theory with eight dynamical flavors
• Infrared fixed point in SU(2) gauge theory with adjoint fermions
• Beta Function and Anomalous Dimensions
• Nonperturbative beta function of twelve-flavor SU(3) gauge theory
• Fundamental partial compositeness
• Infrared Zero of $\beta$ and Value of ${\gamma }_m$ for an SU(3) Gauge Theory at the Five-Loop Level
• Asymptotically Safe Standard Model Extensions?
• Nonperturbative beta function of eight-flavor SU(3) gauge theory
• Conformal Window 2.0: The Large $N_f$ Safe Story
• Study of Possible Ultraviolet Zero of the Beta Function in Gauge Theories with Many Fermions
• Asymptotically Safe Grand Unification
• An Analysis of Scheme Transformations in the Vicinity of an Infrared Fixed Point
• Higher-Order Scheme-Independent Series Expansions of ${\gamma }_{\bar{\psi }\psi ,IR}$ and ${\beta }_{IR}^{\prime }$ in Conformal Field Theories
• The a theorem for Gauge-Yukawa theories beyond Banks-Zaks
• Scheme-Independent Series Expansions at an Infrared Zero of the Beta Function in Asymptotically Free Gauge Theories
• Light Dilaton at Fixed Points and Ultra Light Scale Super Yang Mills
• Scheme Transformations in the Vicinity of an Infrared Fixed Point
• Composite Inflation Setup and Glueball Inflation
• Higher-Loop Structural Properties of the $\beta$ Function in Asymptotically Free Vectorial Gauge Theories
• Scheme-Independent Calculation of ${\gamma }_{\bar{\psi }\psi ,IR}$ for an SU(3) Gauge Theory
• Gauge-Yukawa theories: Beta functions at large $N_f$
• Conformal Behavior at Four Loops and Scheme (In)Dependence
• Study of Scheme Transformations to Remove Higher-Loop Terms in the $\beta$ Function of a Gauge Theory
• MCRG Minimal Walking Technicolor
• Higher-Loop Calculations of the Ultraviolet to Infrared Evolution of a Vectorial Gauge Theory in the Limit $N_c\to \infty$, $N_f\to \infty$ with $N_f/N_c$ Fixed
• Generalized Scheme Transformations for the Elimination of Higher-Loop Terms in the Beta Function of a Gauge Theory
• Consistent Perturbative Fixed Point Calculations in QCD and SQCD
• Comparison of Some Exact and Perturbative Results for a Supersymmetric SU($N_c$) Gauge Theory
• Higher Loop Corrections to the Infrared Evolution of Fermionic Gauge Theories in the RI' Scheme
• Infrared Fixed Points in the minimal MOM Scheme
• Anomalous Dimensions of Conformal Baryons
• Safe Pati-Salam
• Framework for an asymptotically safe Standard Model via dynamical breaking
• Finite size scaling in minimal walking technicolor
• New Scheme Transformations and Application to Study Scheme Dependence of an Infrared Zero of the Beta Function in Gauge Theories
• Quantum Critical Behaviour of Semi-Simple Gauge Theories
• Phase structure of complete asymptotically free SU($N_c$) theories with quarks and scalar quarks
• Infrared Fixed Point Physics in $\mathrm{SO}(N_c)$ and $\mathrm{Sp}(N_c)$ Gauge Theories
• $A_k\bar{F}$ Chiral Gauge Theories
• A Perturbative Realization of Miransky Scaling
• Conformal window from conformal expansion
• Conformal Gauge-Yukawa Theories away From Four Dimensions
• Exceptional and Spinorial Conformal Windows
• Jumping Dynamics
• Physics of the Non-Abelian Coulomb Phase: Insights from Padé Approximants
• Safe Trinification
• Renormalization-Group Flows and Fixed Points in Yukawa Theories
• Scheme-Independent Calculations of Anomalous Dimensions of Baryon Operators in Conformal Field Theories
• On the Ultraviolet to Infrared Evolution of Chiral Gauge Theories
• Higher-Order Scheme-Independent Calculations of Physical Quantities in the Conformal Phase of a Gauge Theory
• On the Question of an Ultraviolet Zero of the Beta Function of the $\lambda ({\vec{\varphi }}^2{)}_4^2$ Theory
• Anomalous dimensions on the lattice
• Scheme-Independent Calculations of Properties at a Conformal Infrared Fixed Point in Gauge Theories with Multiple Fermion Representations
• Safety versus triviality on the lattice
• Running coupling constant and mass anomalous dimension of six-flavor SU(2) gauge theory
• Towards the QED beta function and renormalons at $1/N_f^2$ and $1/N_f^3$
• Asymptotically safe and free chiral theories with and without scalars
• Analysis of a Zero of a Beta Function Using All-Orders Summation of Diagrams
• A complete asymptotically safe embedding of the Standard Model
• Properties of the twisted Polyakov loop coupling and the infrared fixed point in the SU(3) gauge theories
• Analytic Coupling Structure of Large $N_f$ (Super) QED and QCD
• Dual of QCD with One Adjoint Fermion
• An Integral Formalism for the Construction of Scheme Transformations in Quantum Field Theory
• Renormalization-Group Evolution of Chiral Gauge Theories
• Fixed point merger in the SU(N) gauge beta functions
• Thermodynamics of asymptotically safe theories
• Renormalization-Group Behavior of ${\varphi }^3$ Theories in $d=6$ Dimensions
• Renormalization Scheme Dependence and the Renormalization Group Beta Function
• Determination of SU(4)${}_{TC}$ Technicolor Gauge Group from Embedding in Extended Technicolor
• Study of the Renormalization-Group Evolution of $\mathcal{N}=1$ Supersymmetric Gauge Theories Using Padé Approximants
• Scheme-Independent Series for Anomalous Dimensions of Higher-Spin Operators at an Infrared Fixed Point in a Gauge Theory
• Four-Fermion Limit of Gauge-Yukawa Theories
• Ideal Walking Dynamics via a Gauged NJL Model
• Conformal Phase Diagram of Complete Asymptotically Free Theories
• Supersymmetric Extension of Technicolor & Fermion Mass Generation
• Conformal Data of Fundamental Gauge-Yukawa Theories
• Thrust Distribution for 3-Jet Production from $e^{+}{e}^{-}$ Annihilation within the QCD Conformal Window and in QED
• Nonperturbative results for two-index conformal windows
• Renormalization of QCD in the interpolating momentum subtraction scheme at three loops
• ${\beta }_{IR}^{\prime }$ at an Infrared Fixed Point in Chiral Gauge Theories
• A novel scheme for the wave function renormalization of the composite operators
• Large-$N_c$ and Large-$N_F$ Limits of SU($N_c$) Gauge Theories with Fermions in Different Representations
• W' and Z' limits for Minimal Walking Technicolor
• Asymptotic safety in the Litim-Sannino model at four loops
• Dynamical Symmetry Breaking in Chiral Gauge Theories with Direct-Product Gauge Groups
• The running coupling of the minimal sextet composite Higgs model
• On the phase structure of extra-dimensional gauge theories with fermions
• Safe and free instantons
• Duality in a Supersymmetric Gauge Theory From a Perturbative Viewpoint
• Anomalous Dimensions at an Infrared Fixed Point in an SU($N_c$) Gauge Theory with Fermions in the Fundamental and Antisymmetric Tensor Representations
• Technicolor Models with Color-Singlet Technifermions and their Ultraviolet Extensions
• Pseudo Goldstone Bosons Phenomenology in Minimal Walking Technicolor
• Safe Hologram
• A Comparative Study of Criticality Conditions for Anomalous Dimensions using Exact Results in an $\mathcal{N}=1$ Supersymmetric Gauge Theory
• A method for getting a finite $\alpha$ in the IR region from an all-order beta function
• Predictions for LHC from SO(4) MWT
• Vacuum Alignment with more Flavors
• Viscous Conformal Gauge Theories
• Conformal Windows beyond Asymptotic Freedom
• Conformality at large number of fermion flavors and composite Higgs
• IR-conformal gauge theories and composite Higgs