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 K\"ahler parameters leads to over 200 such models which we present. Each of these models has precisely the matter spectrum of the minimal supersymmetric standard model, 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.