Spontaneous Breaking of Scale Invariance and the Ultraviolet Fixed Point inO(N)-Symmetric (φ36) Theory

At large $N$, the $\eta {\overrightarrow{\phi }}^6$ 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 $\frac{1}{N}$ expansion and emphasize the nonperturbative nature of these phenomena.