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) 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. 
Mikhail Shifman, Arkady Vainshtein, Alexei Yung
hep-th