Conformal window from conformal expansion

Abstract

We study the conformal window of asymptotically free gauge theories containing $N_f$ flavors of fermion matter transforming to the vector and two-index representations of $SO(N),SU(N)$ and $Sp(2N)$ gauge groups. For $SO(N)$ we also consider the spinorial representation. We determine the critical number of flavors $N_f^{\mathrm{cr}}$, corresponding to the lower end of the conformal window, by using the conjectured critical condition on the anomalous dimension of the fermion bilinear at an infrared fixed point, ${\gamma }_{\bar{\psi }\psi }=1$ or equivalently ${\gamma }_{\bar{\psi }\psi }(2-{\gamma }_{\bar{\psi }\psi })=1$. To compute the anomalous dimension we employ the Banks-Zaks conformal expansion up to the $4$th order in ${\Delta }_{N_f}=N_f^{\mathrm{AF}}-N_f$ with $N_f^{\mathrm{AF}}$ denoting the onset of the loss of asymptotic freedom, where we show that the latter critical condition provides a better performance along with this conformal expansion. To quantify the uncertainties in our analysis, which potentially originate from nonperturbative effects, we propose two distinct approaches by assuming the large order behavior of the conformal expansion separately, either convergent or divergent asymptotic. In the former case, we take the difference in the Padé approximants to the two definitions of the critical condition, whereas in the latter case the truncation error associated with the singularity in the Borel plane is taken into account. Our results are further compared to other analytical methods as well as lattice results available in the literature. In particular, we find that $SU(2)$ with six and $SU(3)$ with ten fundamental flavors are likely on the lower edge of the conformal window, which are consistent with the recent lattice results. We also predict that $Sp(4)$ theories with fundamental and antisymmetric fermions have the critical numbers of flavors, approximately ten and five, respectively.

arXiv comment22 pages, 9 figures, 3 tables; Version accepted for publication in PRD

References in corpus (58)

• Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories
• The four-loop beta-function in Quantum Chromodynamics
• Renormalons
• Five-Loop Running of the QCD coupling constant
• 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
• The five-loop beta function of Yang-Mills theory with fermions
• Conformality Lost
• Walking, Weak first-order transitions, and Complex CFTs
• A universal result on central charges in the presence of double-trace deformations
• Asymptotic safety guaranteed
• UV descriptions of composite Higgs models without elementary scalars
• A New Constraint on Strongly Coupled Field Theories
• Chiral phase structure of QCD with many flavors
• Supersymmetry Inspired QCD Beta Function
• The five-loop Beta function for a general gauge group and anomalous dimensions beyond Feynman gauge
• UV and IR Zeros of Gauge Theories at The Four Loop Order and Beyond
• The Phase Structure of an SU(N) Gauge Theory with N_f Flavors
• Five-loop renormalisation of QCD in covariant gauges
• Nonperturbative investigations of SU(3) gauge theory with eight dynamical flavors
• The QCD beta-function at O(1/N_f)
• Sp(4) gauge theory on the lattice: towards SU(4)/Sp(4) composite Higgs (and beyond)
• RG Flows and Bifurcations
• Two-flavor adjoint QCD
• Sp(4) gauge theories on the lattice: $N_f=2$ dynamical fundamental fermions
• Large N flavor beta-functions: a recap
• The conformal window in QCD and supersymmetric QCD
• Beta Function and Anomalous Dimensions
• Disentangling running coupling and conformal effects in QCD
• Sp(4) gauge theories on the lattice: Quenched fundamental and antisymmetric fermions
• Infrared Zero of $\beta$ and Value of ${\gamma }_m$ for an SU(3) Gauge Theory at the Five-Loop Level
• Conformal Window 2.0: The Large $N_f$ Safe Story
• 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
• Scheme-Independent Calculation of ${\gamma }_{\bar{\psi }\psi ,IR}$ for an SU(3) Gauge Theory
• Hot Conformal Gauge Theories
• Consistent Perturbative Fixed Point Calculations in QCD and SQCD
• Conformality Loss, Walking, and 4D Complex Conformal Field Theories at Weak Coupling
• Extended investigation of the twelve-flavor $\beta$-function
• Gradient flow step-scaling function for SU(3) with twelve flavors
• Infrared Fixed Point Physics in $\mathrm{SO}(N_c)$ and $\mathrm{Sp}(N_c)$ Gauge Theories
• Near-conformal dynamics in a chirally broken system
• Lattice Gauge Theory for Physics Beyond the Standard Model
• Into the conformal window: multi-representation gauge theories
• Physics of the Non-Abelian Coulomb Phase: Insights from Padé Approximants
• Gradient flow step-scaling function for SU(3) with ten fundamental flavors
• Improved study of the $\beta$-function of $SU(3)$ gauge theory with $N_f=10$ massless domain-wall fermions
• Scheme-Independent Calculations of Anomalous Dimensions of Baryon Operators in Conformal Field Theories
• A possible phase for adjoint QCD
• Higher-Order Scheme-Independent Calculations of Physical Quantities in the Conformal Phase of a Gauge Theory
• Scheme-Independent Calculations of Properties at a Conformal Infrared Fixed Point in Gauge Theories with Multiple Fermion Representations
• Looking through the QCD Conformal Window with Perturbation Theory
• Fixed point merger in the SU(N) gauge beta functions
• Resummation in QFT with Meijer G-functions
• Scheme-Independent Series for Anomalous Dimensions of Higher-Spin Operators at an Infrared Fixed Point in a Gauge Theory
• Conformal expansions and renormalons
• Bifurcations in the RG-flow of QCD

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