Flat directions and spontaneous breaking of scale invariance in a supersymmetric O( N) ×O( N) model

Abstract

The dynamics by which scale invariance can be broken in a theory which has no trace anomalies in erturbation theory is studied. The phase structure of a supersymmetric model with O(N) × O(N) internal symmetry is analyzed. In the large-N limit there is no explicit breaking of scale invariance and the perturbative β function vanishes. The variational ground state energy, which is calculable in the large-N limit, has flat directions which allow spontaneous breaking of scale invariance by non-perturbative generation of mass scales. In a particular phase the breaking of scale invariance is directly related to the breaking of the internal symmetry O(N) ×O(N) →O(N − 1) ×O(N − 1). The massless dilaton and “dilatino” is searched for in the ground state of all phases.