  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) x C^1. We had thoroughly analyzed the latter model
previously, found the exact beta 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 beta functions of our connected (0,2) sigma models.
