Physics of the Non-Abelian Coulomb Phase: Insights from Padé Approximants

Abstract

We consider a vectorial, asymptotically free SU($N_c$) gauge theory with $N_f$ fermions in a representation $R$ having an infrared (IR) fixed point. We calculate and analyze Padé approximants to scheme-independent series expansions for physical quantities at this IR fixed point, including the anomalous dimension, ${\gamma }_{\bar{\psi }\psi ,IR}$, to $O({\Delta }_f^4)$, and the derivative of the beta function, ${\beta }_{IR}^{\prime }$, to $O({\Delta }_f^5)$, where ${\Delta }_f$ is an $N_f$-dependent expansion variable. We consider the fundamental, adjoint, and rank-2 symmetric tensor representations. The results are applied to obtain further estimates of ${\gamma }_{\bar{\psi }\psi ,IR}$ and ${\beta }_{IR}^{\prime }$ for several SU($N_c$) groups and representations $R$, and comparisons are made with lattice measurements. We apply our results to obtain new estimates of the extent of the respective non-Abelian Coulomb phases in several theories. For $R=F$, the limit $N_c\to \infty$ and $N_f\to \infty$ with $N_f/N_c$ fixed is considered. We assess the accuracy of the scheme-independent series expansion of ${\gamma }_{\bar{\psi }\psi ,IR}$ in comparison with the exactly known expression in an $\mathcal{N}=1$ supersymmetric gauge theory. It is shown that an expansion of ${\gamma }_{\bar{\psi }\psi ,IR}$ to $O({\Delta }_f^4)$ is quite accurate throughout the entire non-Abelian Coulomb phase of this supersymmetric theory.

arXiv comment28 pages, 3 figures

References in corpus (81)

• Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories
• Bounding scalar operator dimensions in 4D CFT
• Lectures on supersymmetric gauge theories and electric-magnetic duality
• The 4-loop quark mass anomalous dimension and the invariant quark mass
• Quark Mass Anomalous Dimension to alpha_s**4
• Walking in the SU(N)
• The five-loop beta function of Yang-Mills theory with fermions
• Thermodynamics and bulk viscosity of approximate black hole duals to finite temperature quantum chromodynamics
• Minimal Walking on the Lattice
• Comments on Unparticles
• Fermion Masses and Mixing in Extended Technicolor Models
• UV and IR Zeros of Gauge Theories at The Four Loop Order and Beyond
• What Maxwell Theory in D<>4 teaches us about scale and conformal invariance
• Limit Cycles and Conformal Invariance
• Light composite scalar in eight-flavor QCD on the lattice
• Comparison of the Pade Approximation Method to Perturbative QCD Calculations
• Strongly interacting dynamics and the search for new physics at the LHC
• Higher-Loop Corrections to the Infrared Evolution of a Gauge Theory with Fermions
• Conformal Windows of SU(N) Gauge Theories, Higher Dimensional Representations and The Size of The Unparticle World
• Neutrino Masses in Theories with Dynamical Electroweak Symmetry Breaking
• The infrared dynamics of Minimal Walking Technicolor
• Lattice tests of beyond Standard Model dynamics
• Dynamical Symmetry Breaking of Extended Gauge Symmetries
• Can the nearly conformal sextet gauge model hide the Higgs impostor?
• Three loop MSbar tensor current anomalous dimension in QCD
• On Scale and Conformal Invariance in Four Dimensions
• Non-Perturbative Dynamics in Supersymmetric Gauge Theories
• Lattice Simulations and Infrared Conformality
• Infrared fixed point in SU(2) gauge theory with adjoint fermions
• Light flavor-singlet scalars and walking signals in $N_f=8$ QCD on the lattice
• Dilaton EFT Framework For Lattice Data
• A Critical Behaviour of Anomalous Currents, Electric-Magnetic Universality and CFT_4
• Lattice simulations with eight flavors of domain wall fermions in SU(3) gauge theory
• Lattice study of conformality in twelve-flavor QCD
• Walking signals in Nf=8 QCD on the lattice
• A precise determination of the psibar-psi anomalous dimension in conformal gauge theories
• The conformal window in QCD and supersymmetric QCD
• Extending Chiral Perturbation Theory with an Isosinglet Scalar
• Determining the conformal window: SU(2) gauge theory with N_f = 4, 6 and 10 fermion flavours
• Conformal Window of Gauge Theories with Four-Fermion Interactions and Ideal Walking
• Finite-size scaling tests for spectra in SU(3) lattice gauge theory coupled to 12 fundamental flavor fermions
• Complex-Temperature Singularities of the Susceptibility in the $d=2$ Ising Model. I. Square Lattice
• Infrared Zero of $\beta$ and Value of ${\gamma }_m$ for an SU(3) Gauge Theory at the Five-Loop Level
• Relations between Observables and the Infrared Fixed-Point in QCD
• Mass anomalous dimension in SU(2) with six fundamental fermions
• Fate of the conformal fixed point with twelve massless fermions and SU(3) gauge group
• 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
• Scheme-Independent Series Expansions at an Infrared Zero of the Beta Function in Asymptotically Free Gauge Theories
• A Prediction for the 4-Loop βFunction
• Scheme Transformations in the Vicinity of an Infrared Fixed Point
• Higher-Loop Structural Properties of the $\beta$ Function in Asymptotically Free Vectorial Gauge Theories
• On the particle spectrum and the conformal window
• Scheme-Independent Calculation of ${\gamma }_{\bar{\psi }\psi ,IR}$ for an SU(3) Gauge Theory
• 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
• 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
• Implications of Dynamical Generation of Standard-Model Fermion Masses
• Consistent Perturbative Fixed Point Calculations in QCD and SQCD
• Two-Color Theory with Novel Infrared Behavior
• Mass anomalous dimension in sextet QCD
• Comparison of Some Exact and Perturbative Results for a Supersymmetric SU($N_c$) Gauge Theory
• Chiral phase transition at finite temperature and conformal dynamics in large Nf QCD
• Z Boson Propagator Correction in Technicolor Theories with ETC Effects Included
• Running coupling in SU(2) gauge theory with two adjoint fermions
• The bulk transition of QCD with twelve flavors and the role of improvement
• Finite size scaling in minimal walking technicolor
• Upper bound on the mass anomalous dimension in many-flavor gauge theories: a conformal bootstrap approach
• Banks-Zaks fixed point analysis in momentum subtraction schemes
• Infrared Fixed Point Physics in $\mathrm{SO}(N_c)$ and $\mathrm{Sp}(N_c)$ Gauge Theories
• The spectrum and mass anomalous dimension of SU(2) adjoint QCD with two Dirac flavours
• Lattice Study on quantum-mechanical dynamics of two-color QCD with six light flavors
• Scheme-Independent Calculations of Physical Quantities in an $\mathcal{N}=1$ Supersymmetric Gauge Theory
• 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
• Asymptotic Pade-Approximant Predictions for Renormalization-Group Functions of Massive ${\varphi }^4$ Scalar Field Theory
• Study of the Six-Loop Beta Function of the $\lambda {\varphi }_4^4$ Theory
• The gradient flow running coupling in SU(2) gauge theory with $N_f=8$ fundamental flavors
• On the Question of a Possible Infrared Zero in the Beta Function of the Finite-$N$ Gross-Neveu Model
• Study of the Question of an Ultraviolet Zero in the Six-Loop Beta Function of the O($N$) $\lambda |\vec{\varphi }{|}^4$ Theory

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• Gradient flow step-scaling function for SU(3) with $N_f$ = 6 or 4 fundamental flavors
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