NAHE-based string models with SU(4) X SU(2) X U(1) SO(10) Subgroup

The orbifold GUT doublet-triplet splitting mechanism was discussed in 1994 in the framework of the NAHE-based free fermionic models in which the SO(10) GUT symmetry is broken to SO(6) X SO(4), SU(3) X SU(2) X U(1)^2, or SU(3) X U(1) X SU(2)^2. In this paper we study NAHE-based free fermionic models in which the SO(10) symmetry is broken at the string level to SU(4) X SU(2) X U(1). In addition to the doublet-triplet splitting this case also has the advantage of inducing the doublet-doublet splitting already at the string level. We demonstrate, however, that NAHE-based models with SU(4) X SU(2) X U(1) SO(10) subgroup are not viable. We show that, similarly to the LRS models, and in contrast to the FSU5, PS and SLM models, the SU421 case gives rise to models without an anomalous U(1) symmetry, and discuss the different cases in terms of their N=4 origins.Comment: 25 pages. Standard Latex. Revised version to appear in NP

A Note on a Standard Embedding on Half-Flat Manifolds

It is argued that the ten dimensional solution that corresponds to the compactification of $E_8 \times E_8$ heterotic string theory on a half-flat manifold is the product space-time $R^{1,2} \times Z_7$ where $Z_7$ is a generalized cylinder with $G_2$ riemannian holonomy. Standard embedding on $Z_7$ then implies an embedding on the half-flat manifold which involves the torsionful connection rather than the Levi-Civita connection. This leads to the breakdown of $E_8 \times E_8$ to $E_6 \times E_8$, as in the case of the standard embedding on Calabi-Yau manifolds, which agrees with the result derived recently by Gurrieri, Lukas and Micu (arXiv:0709.1932) using a different approach. Green-Schwarz anomaly cancellation is then implemented via the torsionful connection on half-flat manifolds.Comment: 5 pages. v2: 6 pages; slightly reworded; version submitted for publication. v3: uses JHEP3.cls, hence 14 pages now. Essentially same content as before. Article in title changed in accordance with JHEP editor's suggestion. Version to appear in JHE