All known examples of four-dimensional quantum field theories with asymptotic freedom or asymptotic safety at weak coupling involve non-Abelian gauge interactions. We demonstrate that this is not a coincidence: No weakly coupled fixed points, ultraviolet or otherwise, can be reliably generated in theories lacking gauge interactions. Implications for particle physics, critical phenomena, and conformal field theory are indicated.
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Bond et al. (2019) studied this question.
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