Theorems for Asymptotic Safety of Gauge Theories

Abstract

We classify the weakly interacting fixed points of general gauge theories coupled to matter and explain how the competition between gauge and matter fluctuations gives rise to a rich spectrum of high- and low-energy fixed points. The pivotal role played by Yukawa couplings is emphasized. Necessary and sufficient conditions for asymptotic safety of gauge theories are also derived, in conjunction with strict no go theorems. Implications for phase diagrams of gauge theories and physics beyond the Standard Model are indicated.

21 pages, 5 figures, 3 tables. v2: results for supersymmetry added; to appear (EPJC)

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• Asymptotic safety guaranteed
• Softened Gravity and the Extension of the Standard Model up to Infinite Energy
• A Very Light Dilaton
• Stable Asymptotically Free Extensions (SAFEs) of the Standard Model
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