Abstract
It has recently been realised that polystable, holomorphic sums of line bundles over smooth Calabi-Yau three-folds provide a fertile ground for heterotic model building. Large numbers of phenomenologically promising such models have been constructed for various classes of Calabi-Yau manifolds. In this paper we focus on a case study for the tetra-quadric - a Calabi-Yau hypersurface embedded in a product of four CP1 spaces. We address the question of finiteness of the class of consistent and physically viable line bundle models constructed on this manifold. Further, for a specific semi-realistic example, we explore the embedding of the line bundle sum into the larger moduli space of non-Abelian bundles, both by means of constructing specific polystable non-Abelian bundles and by turning on VEVs in the associated low-energy theory. In this context, we explore the fate of the Higgs doublets as we move in bundle moduli space. The non-Abelian compactifications thus constructed lead to SU(5) GUT models with an additional global B-L symmetry. The non-Abelian compactifications inherit many of the appealing phenomenological features of the Abelian model, such as the absence of dimension four and dimension five operators triggering fast proton decay.
Highlights
Smooth Calabi-Yau compactifications of the heterotic string and M-theory represent one of the classic and most-developed avenues from string theory to low energy physics [1]
We have presented an in-depth analysis of various aspects of heterotic line bundle models, in the context of a “case-study” for the tetra-quadric Calabi-Yau hypersurface in (CP1)×4
We have studied the question of finiteness of the class of heterotic line bundle models; mathematically this corresponds to the question of finiteness of polystable line bundles sums with fixed total Chern class
Summary
Smooth Calabi-Yau compactifications of the heterotic string and M-theory represent one of the classic and most-developed avenues from string theory to low energy physics [1]. Perhaps the most important issue is to understand how a given line bundle model is embedded into the larger moduli space of non-Abelian bundles and we will study this question for the aforementioned model on the tetra-quadric This problem can be approached in two complementary ways. This means that the Higgs doublets remain massless as we continue away from the Abelian locus to an SU(5) × UX (1) model These examples demonstrate the power and the advantage of the present approach: we start with an Abelian model which is easier to construct and analyse, but the symmetries which arise at the Abelian locus lead to some degree of control as to which couplings will or will not appear as we move into the non-Abelian part of the moduli space. The breaking to the Standard Model is only discussed briefly in section 5, to illustrate the virtues of the chosen line bundle model and will be presented in detail elsewhere
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