Two Hundred Heterotic Standard Models on Smooth Calabi-Yau Threefolds

TL;DR

This work develops a large, explicit set of heterotic string vacua built from Abelian line-bundle sums on smooth Calabi-Yau threefolds, achieving MSSM-like spectra with full global consistency. By algorithmically scanning complete intersection Calabi-Yau manifolds with $h^{1,1}(X)\le 5$, the authors extract 208 models that yield the MSSM matter content, at least one Higgs pair, and either the exact SM gauge group or a massless $U(1)$ that can be broken by singlet VEVs. The four additional $U(1)$ factors from $S(U(1)^5)$ are mostly lifted via the Green-Schwarz mechanism, leaving a rich phenomenology controlled by residual global symmetries and bundle-moduli vevs, influencing proton stability, the $\mu$-term, Yukawa textures, and neutrino masses. The results demonstrate a scalable, globally consistent framework for string phenomenology, enabling systematic studies across a extensive machinery of Yukawa couplings, proton decay channels, and neutrino physics, with extensions to larger $h^{1,1}$ and other CY constructions planned.

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 Kahler 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, naively, four additional U(1) symmetries, however these 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.