More on two-dimensional O (N) models with N = (0,1) supersymmetry

We study the behavior of two-dimensional supersymmetric connections of n copies of O(N) models with an N = (0,1) heterotic deformation generated by a right-moving fermion. We develop the model in analogy with the connected N=(0,2) CP(N-1) models for the case of a single connecting fermionic superfield. We calculate the effective potential in the large-N limit and determine the vacuum field configurations. Similarly to other supersymmetry (SUSY) connected models we find that SUSY is unbroken under certain conditions despite the vanishing of the Witten index. Specifically, this preservation of SUSY occurs when we have an even number n of O(N) families. As in previous cases we show that this result follows from a Z_n symmetry under a particular exchange of the O(N) families. This leads to a definition of a modified Witten index, which guarantees the preservation of SUSY in this case.