Chiral supersymmetric Standard Model spectra from orientifolds of Gepner models

We construct d=4, N=1 orientifolds of Gepner models with just the chiral spectrum of the Standard Model. We consider all simple current modular invariants of c=9 tensor products of N=2 minimal models. For some very specific tensor combinations, and very specific modular invariants and orientifold projections, we find a large number of such spectra. We allow for Standard Model singlet (dark) matter and non-chiral exotics. The Chan-Paton gauge group is either U(3)×Sp(2)×U(1)×U(1) or U(3)×U(2)×U(1)×U(1). In many cases the Standard Model hypercharge U(1) has no coupling to RR 2-forms and hence remains massless; in some of those models the B-L gauge boson does acquire a mass.