Higher-Order Scheme-Independent Calculations of Physical Quantities in the Conformal Phase of a Gauge Theory

Abstract

We consider an asymptotically free vectorial SU($N_c$) gauge theory with $N_f$ massless fermions in a representation $R$, having an infrared fixed point (IRFP) of the renormalization group at ${\alpha }_{IR}$ in the conformal non-Abelian Coulomb phase. The cases with $R$ equal to the fundamental, adjoint, and symmetric rank-2 tensor representation are considered. We present scheme-independent calculations of the anomalous dimension ${\gamma }_{\bar{\psi }\psi ,IR}$ to $O({\Delta }_f^4)$ and ${\beta }_{IR}^{\prime }$ to $O({\Delta }_f^5)$ at this IRFP, where ${\Delta }_f$ is an $N_f$-dependent expansion parameter. Comparisons are made with conventional $n$-loop calculations and lattice measurements. As a test of the accuracy of the ${\Delta }_f$ expansion, we calculate ${\gamma }_{\bar{\psi }\psi ,IR}$ to $O({\Delta }_f^3)$ in $\mathcal{N}=1$ SU($N_c$) supersymmetric quantum chromodynamics and find complete agreement, to this order, with the exactly known expression. The ${\Delta }_f$ expansion also avoids a problem in which an IRFP may not be manifest as an IR zero of a higher $n$-loop beta function.

6 pages, latex, 3 figures

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• 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
• Scheme-Independent Calculations of Physical Quantities in an $\mathcal{N}=1$ Supersymmetric Gauge Theory
• Scheme-Independent Calculations of Properties at a Conformal Infrared Fixed Point in Gauge Theories with Multiple Fermion Representations
• Infrared fixed point of SU(2) gauge theory with six flavors
• Scheme-Independent Series for Anomalous Dimensions of Higher-Spin Operators at an Infrared Fixed Point in a Gauge Theory
• Slope of the beta function at the fixed point of SU(2) gauge theory with six or eight flavors
• ${\beta }_{IR}^{\prime }$ at an Infrared Fixed Point in Chiral Gauge Theories
• 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
• Renormalization Scheme Dependence of $\beta$-Functions In Lorentz-Violating Quantum Field Theory
• A Comparative Study of Criticality Conditions for Anomalous Dimensions using Exact Results in an $\mathcal{N}=1$ Supersymmetric Gauge Theory