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Register a new userAsymmetric Gepner Models II. Heterotic Weight Lifting
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A systematic study of lifted Gepner models is presented. Lifted Gepner models are obtained from standard Gepner models by replacing one of the N=2 building blocks and the $E_8$ factor by a modular isomorphic $N=0$ model on the bosonic side of the heterotic string. The main result is that after this change three family models occur abundantly, in sharp contrast to ordinary Gepner models. In particular, more than 250 new and unrelated moduli spaces of three family models are identified. We discuss the occurrence of fractionally charged particles in these spectra.
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In the same spirit as heterotic weight lifting, B-L lifting is a way of replacing the superfluous and ubiquitous U(1)_{B-L} with something else with the same modular properties, but different conformal weights and ground state dimensions. This method works in principle for all variants of (2,2) constructions, such as orbifolds, Calabi-Yau manifolds, free bosons and fermions and Gepner models, since it only modifies the universal SO(10) x E_8 part of the CFT. However, it can only yield chiral spectra if the ``internal sector of the theory provides a simple current of order 5. Here we apply this new method to Gepner models. Including exceptional invariants, 86 of them have the required order 5 simple current, and 69 of these yield chiral spectra. Three family spectra occur abundantly.
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.
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.
Using Z3 asymmetric orbifolds in heterotic string theory, we construct N=1 SUSY three-generation models with the standard model gauge group SU(3)_C times SU(2)_L times U(1)_Y and the left-right symmetric group SU(3)_C times SU(2)_L times SU(2)_R times U(1)_{B-L}. One of the models possesses a gauge flavor symmetry for the Z3 twisted matter.
We study heterotic asymmetric orbifold models. By utilizing the lattice engineering technique, we classify (22,6)-dimensional Narain lattices with right-moving non-Abelian group factors which can be starting points for Z3 asymmetric orbifold construction. We also calculate gauge symmetry breaking patterns.
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