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We present a class of smooth supersymmetric heterotic solutions with a non-compact Eguchi-Hanson space. The non-compact geometry is embedded as the base of a six-dimensional non-Kahler manifold with a non-trivial torus fiber. We solve the non-linear anomaly equation in this background exactly. We also define a new charge that detects the non-Kahlerity of our solutions.
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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.
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.
We present a novel string-derived $U(1)$ combination that satisfies necessary properties to survive to low scales. We discuss previous attempts at acquiring such an abelian gauge symmetry from two different string embeddings and the pitfalls associated with them. Finally, we give an example of how a satisfactory model may be constructed within our framework.
Grand unification groups (GUTs) are constructed from SO(32) heterotic string via $Z_{12-I}$ orbifold compactification. So far, most phenomenological studies from string compactification relied on $EE8$ heterotic string, and this invites the SO(32) heterotic string very useful for future phenomenological studies. Here, spontaneous symmetry breaking is achieved by Higgsing of the anti-symmetric tensor representations of SU($N$). The anti-SU($N$) presented in this paper is a completely different class from the flipped-SU($N$)s from the spinor representations of SO($2N$). Here, we realize chiral representations: $tsixoplus 5cdot ineb $ for a SU(9) GUT and $3{{ten}_Loplus {fiveb}_L}$ for a SU(5)$$ GUT. In particular, we confirm that the non-Abelian anomalies of SU(9) gauge group vanish and hence our compactification scheme achieves the key requirement. We also present the Yukawa couplings, in particular for the heaviest fermion, $t$, and lightest fermions, neutrinos. In the supersymmetric version, we present a scenario how supersymmetry can be broken dynamically via the confining gauge group SU(9). Three families in the visible sector are interpreted as the chiral spectra of SU(5)$$ GUT.
In this paper we define and study a matrix model describing the M-theory plane wave background with a single Horava-Witten domain wall. In the limit of infinite mu, the matrix model action becomes quadratic and we can identify the matrix Hamiltonian with a regularized Hamiltonian for hemispherical membranes that carry fermionic degrees of freedom on their boundaries. The number of fermionic degrees of freedom must be sixteen; this condition arises naturally in the framework of the matrix model. We can also prove the exact E_8 symmetry of the spectrum around the membrane vacua at infinite mu, which arises as a current algebra at level one just as in the heterotic string. We also find the full E_8 gauge multiplet as well as the multiple-gluon states, carried by collections of hemispherical membranes. Finally we discuss the dual description of the hemispherical membranes in terms of spherical fivebranes immersed in the domain wall; we identify the correct vacuum of the matrix model and make some preliminary comparisons with the (1,0) superconformal field theory.
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