We present supersymmetric, tadpole-free d = 4, N = 1 orientifold vacua with a three family chiral fermion spectrum that is identical to that of the Standard Model. Starting with all simple current orientifolds of all Gepner models we perform a systematic search for such spectra. We consider several variations of the standard four-stack intersecting brane realization of the standard model, with all quarks and leptons realized as bifundamentals and perturbatively exact baryon and lepton number symmetries, and with a U (1) Y vector boson that does not acquire a mass from Green-Schwarz terms. The number of supersymmetric Higgs pairs H 1 + H 2 is left free. In order to cancel all tadpoles, we allow a "hidden" gauge group, which must be chirally decoupled from the standard model. We also allow for non-chiral mirror-pairs of quarks and leptons, non-chiral exotics and (possibly chiral) hidden, standard model singlet matter, as well as a massless B-L vector boson. All of these less desirable features are absent in some cases, although not simultaneously. In particular, we found cases with massless Chan-Paton gauge bosons generating nothing more than SU (3) × SU (2) × U (1). We obtain almost 180000 rationally distinct solutions (not counting hidden sector degrees of freedom), and present distributions of various quantities. We analyse the tree level gauge couplings, and find a large range of values, remarkably centered around the unification point.

Universal formulas for the boundary and crosscap coefficients are presented, which are valid for all symmetric simple current modifications of the charge conjugation invariant of any rational conformal field theory.

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. 4 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.1 email:tdykstra@nikhef.nl 2 email:lennaert@itf.fys.leuven.ac.be 3 email:t58@nikhef.nl 4 Updated and almost complete results are available at www.nikhef.nl/∼t58/Orientifold results.ps.

The standard Klein bottle coefficient in the construction of open descendants is shown to equal the Frobenius-Schur indicator of a conformal field theory. Other consistent Klein bottle projections are shown to correspond to simple currents. These observations enable us to generalize the standard open string construction from C-diagonal parent theories to include non-standard Klein bottles. Using (generalizations of) the Frobenius-Schur indicator we prove positivity and integrality of the resulting open and closed string state multiplicities for standard as well as non-standard Klein bottles.

We analyze unoriented Wess-Zumino-Witten models from a geometrical point of view. We show that the geometric interpretation of simple current crosscap states is as centre orientifold planes localized on conjugacy classes of the group manifold. We determine the locations and dimensions of these planes for arbitrary simply-connected groups and orbifolds thereof. The dimensions of the O-planes turn out to be given by the dimensions of symmetric coset manifolds based on regular embeddings. Furthermore, we give a geometrical interpretation of boundary conjugation in open unoriented WZW models; it yields D-branes together with their images under the orientifold projection. To find the agreement between O-planes and crosscap states, we find explicit answers for lattice extensions of Gaussian sums. These results allow us to express the modular P -matrix, which is directly related to the crosscap coefficient, in terms of characters of the horizontal subgroup of the affine Lie algebra. A corollary of this relation is that there exists a formal linear relation between the modular P -and the modular S-matrix.