Two hundred heterotic standard models on smooth Calabi-Yau threefolds

Abstract

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.

Matter in transition

“…Matching these parameters gives a clear picture of the duality between these classes of models and illuminates many features such as the appearance of SCFTs at the transition points and the matching of constraints between the two pictures. We view this work as important first step into extending heterotic/F-theory duality to include more complex and phenomenologically relevant Calabi-Yau geometries and vector bundles (including, for example the geometries in [85][86][87][88] which involve bundles with reducible structure groups and Green-Schwarz massive U(1) symmetries).…”

The moduli space of heterotic line bundle models: a case study for the tetra-quadric

“…The line bundle construction has been extensively discussed in refs. [7,8] and, below, we summarise its most important features, including the derivation of the GUT spectrum. Knowledge of the GUT spectrum will be crucial for the comparison between Abelian and non-Abelian compactifications in section 6.…”

“…However, only recently extensive scans over heterotic Calabi-Yau compactifications with line bundle sums could be envisaged [7][8][9][10]. The heterotic line bundle models considered in these publications are based on rank four or five Abelian vector bundles over smooth Calabi-Yau three-folds with non-trivial fundamental group.…”

“…Recently, this situation has changed. In a series of publications [7][8][9][10], a promising class of E 8 × E 8 heterotic compactifications, based on line bundle sums, has been proposed and analysed. Line bundle sums have been previously considered as viable heterotic gauge backgrounds in [11][12][13][14].…”

“…Specifically, in refs. [7,8] over 200 SU(5) GUT models were constructed on discrete quotients of complete intersection Calabi-Yau manifolds. All these have precisely three generations of GUT families, no anti-families, at least one 5 − 5 pair of Higgs fields and no other matter charged under the GUT group.…”