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Register a new userChiral Supersymmetric Standard Model Spectra from Orientifolds of Gepner Models
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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) x Sp(2) x U(1) x U(1) or U(3) x U(2) x U(1) x 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.
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We summarize recent progress in constructing orientifolds of Gepner models, a phenomenologically interesting class of exactly solvable string compactifications with viable gauge groups and chiral matter.
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 intersection 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 bechirally 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) x SU(2) x 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.
The embedding of the SM hypercharge into an orientifold gauge group is studied. Possible embeddings are classified, and a systematic construction of bottom-up configurations and top-down orientifold vacua is achieved, solving the tadpole conditions in the context of Gepner orientifolds. Some hypercharge embeddings are strongly preferred compared to others. Configurations with chiral antisymmetric tensors are suppressed. We find among others, genuine examples of supersymmetric SU(5), flipped SU(5), Pati-Salam and trinification vacua with no chiral exotics.
We reconsider a class of heterotic string theories studied in 1989, based on tensor products of N=2 minimal models with asymmetric simple current invariants. We extend this analysis from (2,2) and (1,2) spectra to (0,2) spectra with SO(10) broken to the Standard Model. In the latter case the spectrum must contain fractionally charged particles. We find that in nearly all cases at least some of them are massless. However, we identify a large subclass where the fractional charges are at worst half-integer, and often vector-like. The number of families is very often reduced in comparison to the 1989 results, but there are no new tensor combinations yielding three families. All tensor combinations turn out to fall into two classes: those where the number of families is always divisible by three, and those where it is never divisible by three. We find an empirical rule to determine the class, which appears to extend beyond minimal N=2 tensor products. We observe that distributions of physical quantities such as the number of families, singlets and mirrors have an interesting tendency towards smaller values as the gauge groups approaches the Standard Model. We compare our results with an analogous class of free fermionic models. This displays similar features, but with less resolution.Finally we present a complete scan of the three family models based on the triply-exceptional combination (1,16*,16*,16*) identified originally by Gepner. We find 1220 distinct three family spectra in this case, forming 610 mirror pairs. About half of them have the gauge group SU(3) x SU(2)_L x SU(2)_R x U(1)^5, the theoretical minimum, and many others are trinification models.
We study orbifolds by permutations of two identical N=2 minimal models within the Gepner construction of four dimensional heterotic strings. This is done using the new N=2 supersymmetric permutation orbifold building blocks we have recently developed. We compare our results with the old method of modding out the full string partition function. The overlap between these two approaches is surprisingly small, but whenever a comparison can be made we find complete agreement. The use of permutation building blocks allows us to use the complete arsenal of simple current techniques that is available for standard Gepner models, vastly extending what could previously be done for permutation orbifolds. In particular, we consider (0,2) models, breaking of SO(10) to subgroups, weight-lifting for the minimal models and B-L lifting. Some previously observed phenomena, for example concerning family number quantization, extend to this new class as well, and in the lifted models three family models occur with abundance comparable to two or four.
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