Price of Asymptotic Safety

Abstract

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.

Comments: 4 pages, 1 table. v2: discussion and outlook expanded, references added, to appear with PRL