Abstract
Compactifications of heterotic theories on smooth Calabi-Yau manifolds remains one of the most promising approaches to string phenomenology. In two previous papers, http://arXiv.org/abs/arXiv:1106.4804 and http://arXiv.org/abs/arXiv:1202.1757, large classes of such vacua were constructed, using sums of line bundles over complete intersection Calabi-Yau manifolds in products of projective spaces that admit smooth quotients by finite groups. A total of 10^12 different vector bundles were investigated which led to 202 SU(5) Grand Unified Theory (GUT) models. With the addition of Wilson lines, these in turn led, by a conservative counting, to 2122 heterotic standard models. In the present paper, we extend the scope of this programme and perform an exhaustive scan over the same class of models. A total of 10^40 vector bundles are analysed leading to 35,000 SU(5) GUT models. All of these compactifications have the right field content to induce low-energy models with the matter spectrum of the supersymmetric standard model, with no exotics of any kind. The detailed analysis of the resulting vast number of heterotic standard models is a substantial and ongoing task in computational algebraic geometry.
Highlights
Programme in the context of smooth Calabi-Yau compactifications of the heterotic string
What lies in front of the heterotic string model builder is a set of highly non-trivial challenges that can be summarised in the following checklist: 1. Construct a geometrical set-up, such that the 4-dimensional compactification of the N = 1 supergravity limit of the heterotic string contains the symmetry SU(3) × SU(2) × U(1) of the Standard Model of particle physics
This step is usually realised in two stages, by firstly breaking the E8 heterotic symmetry to a Grand Unified Theory (GUT) group and breaking the latter to the Standard Model gauge group (plus possibly U(1) factors)
Summary
The structure of E8 × E8 heterotic compactifications on smooth Calabi-Yau three-folds with Abelian vector bundles, as well as the class of N = 1 four dimensional supergravities to which they lead, have been thoroughly discussed in two previous publications [40, 41]. We limit the scope of this section to merely summarising the central features of heterotic line bundle standard models. We provide a discussion on the possible structure groups of vector bundles constructed as direct sums of holomorphic line bundles
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