Consistent Perturbative Fixed Point Calculations in QCD and SQCD

Abstract

We suggest how to consistently calculate the anomalous dimension ${\gamma }_{\ast }$ of the $\bar{\psi }\psi$ operator in finite order perturbation theory at an infrared fixed point for asymptotically free theories. If the $n+1$ loop beta function and $n$ loop anomalous dimension are known then ${\gamma }_{\ast }$ can be calculated exactly and fully scheme independently through $O({\Delta }_f^n)$ where ${\Delta }_f=\overline{N_f}-N_f$ and $N_f$ is the number of flavors and ${\bar{N}}_f$ is the number of flavors above which asymptotic freedom is lost. For a supersymmetric theory the calculation preserves supersymmetry order by order in ${\Delta }_f$. We then compute ${\gamma }_{\ast }$ through $O({\Delta }_f^2)$ for supersymmetric QCD in the $\overline{\text{DR}}$ scheme and find that it matches the exact known result. We find that ${\gamma }_{\ast }$ is astonishingly well described in perturbation theory already at the few loops level throughout the entire conformal window. We finally compute ${\gamma }_{\ast }$ through $O({\Delta }_f^3)$ for QCD and a variety of other non-supersymmetric fermionic gauge theories. Small values of ${\gamma }_{\ast }$ are observed for a large range of flavors.

12 pages, 3 figures

References in corpus (6)

• Higher-Loop Corrections to the Infrared Evolution of a Gauge Theory with Fermions
• Beta Function and Anomalous Dimensions
• Conformal Behavior at Four Loops and Scheme (In)Dependence
• Comparison of Some Exact and Perturbative Results for a Supersymmetric SU($N_c$) Gauge Theory
• Banks-Zaks fixed point analysis in momentum subtraction schemes
• Analysis of a Zero of a Beta Function Using All-Orders Summation of Diagrams

Cited by in corpus (28)

• Extending Chiral Perturbation Theory with an Isosinglet Scalar
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• Infrared Zero of $\beta$ and Value of ${\gamma }_m$ for an SU(3) Gauge Theory at the Five-Loop Level
• Nonperturbative beta function of eight-flavor SU(3) gauge theory
• 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
• Anomalous Dimensions of Conformal Baryons
• Infrared Fixed Point Physics in $\mathrm{SO}(N_c)$ and $\mathrm{Sp}(N_c)$ Gauge Theories
• Conformal window from conformal expansion
• Physics of the Non-Abelian Coulomb Phase: Insights from Padé Approximants
• Into the conformal window: multi-representation gauge theories
• Scheme-Independent Calculations of Anomalous Dimensions of Baryon Operators in Conformal Field Theories
• A possible phase for adjoint QCD
• 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
• Scheme-Independent Calculations of Properties at a Conformal Infrared Fixed Point in Gauge Theories with Multiple Fermion Representations
• An Integral Formalism for the Construction of Scheme Transformations in Quantum Field Theory
• Scheme-Independent Series for Anomalous Dimensions of Higher-Spin Operators at an Infrared Fixed Point in a Gauge Theory
• Renormalization-Group Behavior of ${\varphi }^3$ Theories in $d=6$ Dimensions
• Conformal Phase Diagram of Complete Asymptotically Free Theories
• Renormalization of QCD in the interpolating momentum subtraction scheme at three loops
• ${\beta }_{IR}^{\prime }$ at an Infrared Fixed Point in Chiral Gauge Theories
• Large-$N_c$ and Large-$N_F$ Limits of SU($N_c$) Gauge Theories with Fermions in Different Representations
• Effect of Scheme Transformations on a Beta Function with Vanishing One-Loop Term
• 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
• A Comparative Study of Criticality Conditions for Anomalous Dimensions using Exact Results in an $\mathcal{N}=1$ Supersymmetric Gauge Theory