Scheme-Independent Series for Anomalous Dimensions of Higher-Spin Operators at an Infrared Fixed Point in a Gauge Theory

Abstract

We consider an asymptotically free vectorial gauge theory, with gauge group $G$ and $N_f$ fermions in a representation $R$ of $G$, having an infrared fixed point of the renormalization group. We calculate scheme-independent series expansions for the anomalous dimensions of higher-spin bilinear fermion operators at this infrared fixed point up to $O({\Delta }_f^3)$, where ${\Delta }_f$ is an $N_f$-dependent expansion variable. Our general results are evaluated for several special cases, including the case $G=\mathrm{SU}(N_c)$ with $R$ equal to the fundamental and adjoint representations.

22 pages, latex, 7 figures

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• Conformal window from conformal expansion
• Renormalization-Group Behavior of ${\varphi }^3$ Theories in $d=6$ Dimensions
• 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