Asymptotic freedom in certain $SO(N)$ and $SU(N)$ models

Abstract

We calculate the $\beta$-functions for $SO(N)$ and $SU(N)$ gauge theories coupled to adjoint and fundamental scalar representations, correcting long-standing, previous results. We explore the constraints on $N$ resulting from requiring asymptotic freedom for all couplings. When we take into account the actual allowed behavior of the gauge coupling, the minimum value of $N$ in both cases turns out to be larger than realized in earlier treatments. We also show that in the large $N$ limit, both models have large regions of parameter space corresponding to total asymptotic freedom.

8 pages, no figures. v6: Minor nonsubstantive changes in text and formatting

References in corpus (7)

• Softened Gravity and the Extension of the Standard Model up to Infinite Energy
• Naturalness and Dimensional Transmutation in Classically Scale-Invariant Gravity
• Theorems for Asymptotic Safety of Gauge Theories
• Stable Asymptotically Free Extensions (SAFEs) of the Standard Model
• Induced Gravity I: Real Scalar Field
• Induced Gravity II: Grand Unification
• The Gauss-Bonnet Coupling Constant in Classically Scale-Invariant Gravity

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