Superconformal anomaly free models in D=4

A family of modified $(0,1)$ heterotic string models in D=4 is constructed in which the strings incorporate $R$ flux tubes which may in special cases support a local spacetime superconformal symmetry consistent with quantum mechanics. There is an intrinsic Goldstino multiplet, so that supersymmetry breaking can be driven by any process that generates a non-zero value for the superpotential. The superconformal anomaly freedom of these models may be related to a naturally vanishing $\Lambda$. The $R$ charge of such models may also play a role in producing a generation-ordered fermion spectrum. \