Critical surfaces and flat directions in a finite theory.

Abstract

We discuss the phase structure of an O(N)\ifmmode\times\else\texttimes\fi{}O(N)-symmetric model with scalar fields in three-dimensional space-time. The effective potential of the theory is calculated in the large-N limit and stability conditions for the model are given. Spontaneous breaking of scale invariance due to the breakdown of the internal symmetry or to nonperturbative mass generation is observed on a critical surface, in connection with the appearance of flat directions in the effective potential. The ground-state energy of the model remains unchanged under the transition from the scale-invariant phase to the various phases, where scale invariance is spontaneously broken. The critical surface allows for arbitrary ratios between the scales associated with breaking of the internal and scale symmetries.