Making supersymmetric connected N= (0,2) sigma models

We construct "connected" (0, 2) sigma models starting from n copies of (2, 2) CP(N-1) models. General aspects of models of this type (known as T+O deformations) had been previously studied in the context of heterotic string theories. Our construction presents a natural generalization of the nonminimally deformed (2, 2) model with an extra (0, 2) fermion superfield on tangent bundle T[CP(N-1)×C1]. We had thoroughly analyzed the latter model previously and found the exact β function and a spontaneous breaking of supersymmetry. In contrast, in certain connected sigma models the spontaneous breaking of supersymmetry disappears. We study the connected sigma models in the large-N limit finding supersymmetric vacua and determining the particle spectrum. While the Witten index vanishes in all the models under consideration, in these special cases of connected models, one can use a permutation symmetry to define a modification of the Witten index which does not vanish. This eliminates the spontaneous breaking of supersymmetry. We then examine the exact β functions of our connected (0, 2) sigma models.