We construct heterotic standard models by compactifying on smooth Calabi-Yau three-folds in the presence of purely Abelian internal gauge fields. A systematic search over complete intersection Calabi-Yau manifolds with less than six Kähler parameters leads to over 200 such models which we present. Each of these models has precisely the matter spectrum of the MSSM, at least one pair of Higgs doublets, the standard model gauge group and no exotics. For about 100 of these models there are four additional U(1) symmetries which are Green-Schwarz anomalous and, hence, massive. In the remaining cases, three U(1) symmetries are anomalous while the fourth, massless one can be spontaneously broken by singlet vacuum expectation values. The presence of additional global U(1) symmetries, together with the possibility of switching on singlet vacuum expectation values, leads to a rich phenomenology which is illustrated for a particular example. Our database of standard models, which can be further enlarged by simply extending the computer-based search, allows for a detailed and systematic phenomenological analysis of string standard models, covering issues such as the structure of Yukawa couplings, R-parity violation, proton stability and neutrino masses.

In a previous publication, arXiv:1106.4804, we have found 200 models from heterotic Calabi-Yau compactifications with line bundles, which lead to standard models after taking appropriate quotients by a discrete symmetry and introducing Wilson lines. In this paper, we construct the resulting standard models explicitly, compute their spectrum including Higgs multiplets, and analyze some of their basic properties. After removing redundancies we find about 400 downstairs models, each with the precise matter spectrum of the supersymmetric standard model, with one, two or three pairs of Higgs doublets and no exotics of any kind. In addition to the standard model gauge group, up to four Green-Schwarz anomalous U(1) symmetries are present in these models, which constrain the allowed operators in the four-dimensional effective supergravity. The vector bosons associated to these anomalous U(1) symmetries are massive. We explicitly compute the spectrum of allowed operators for each model and present the results, together with the defining data of the models, in a database of standard models accessible here. Based on these results we analyze elementary phenomenological properties. For example, for about 200 models all dimension four and five proton decay violating operators are forbidden by the additional U(1) symmetries.

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.Comment: 33 pages, Late

In this work we systematically enumerate genus one fibrations in the class of 7, 890 Calabi-Yau manifolds defined as complete intersections in products of projective spaces, the so-called CICY threefolds. This survey is independent of the description of the manifolds and improves upon past approaches that probed only a particular algebraic form of the threefolds (i.e. searches for "obvious" genus one fibrations as in [1,2]). We also study K3-fibrations and nested fibration structures. That is, K3 fibrations with potentially many distinct elliptic fibrations. To accomplish this survey a number of new geometric tools are developed including a determination of the full topology of all CICY threefolds, including triple intersection numbers. In 2, 946 cases this involves finding a new "favorable" description of the manifold in which all divisors descend from a simple ambient space. Our results consist of a survey of obvious fibrations for all CICY threefolds and a complete classification of all genus one fibrations for 4, 957 "Kähler favorable" CICYs whose Kähler cones descend from a simple ambient space. Within the CICY dataset, we find 139, 597 obvious genus one fibrations, 30, 974 obvious K3 fibrations and 208, 987 nested combinations. For the Kähler favorable geometries we find a complete classification of 377, 559 genus one fibrations. For one manifold with Hodge numbers (19, 19) we find an explicit description of an infinite number of distinct genus-one fibrations extending previous results for this particular geometry that have appeared in the literature. The data associated to this scan is available here [3].

We approach string phenomenology from the perspective of computational algebraic geometry, by providing new and efficient techniques for proving stability and calculating particle spectra in heterotic compactifications. This is done in the context of complete intersection Calabi-Yau manifolds in a single projective space where we classify positive monad bundles. Using a combination of analytic methods and computer algebra we prove stability for all such bundles and compute the complete particle spectrum, including gauge singlets. In particular, we find that the number of anti-generations vanishes for all our bundles and that the spectrum is manifestly moduli-dependent. anderson@maths.ox.ac.uk