Spontaneous Breaking of Scale Invariance and the Ultraviolet Fixed Point in O (N)-Symmetric (36) Theory

At large N, the 6 theory is shown to possess a nontrivial ultraviolet fixed point. A new phase is found where asymptotic scale invariance is spontaneously broken and a dynamical mass is generated through dimensional transmutation. At the tricritical limit, the spontaneous breaking of an exact scale invariance at leading N results in the formation of a massless composite Goldstone mode, the dilaton. We compare these results to standard 1N expansion and emphasize the nonperturbative nature of these phenomena. © 1984 The American Physical Society