Heterotic Line Bundle Standard Models

TL;DR

The paper constructs and analyzes a large class of heterotic line bundle standard models in four dimensions, starting from Abelian split bundles that yield the gauge group $G_{ m SM} imes S(U(1)^5)$ and a MSSM-like spectrum after quotienting by discrete symmetries and Wilson lines. It provides a detailed four-dimensional effective theory description, including the superpotential, Kahler potential, D-terms, anomaly cancellation via Green–Schwarz mechanisms, and the masses of anomalous U(1) gauge bosons, and then connects this to explicit downstairs models on CICYs with calculable cohomology and Yukawa data. The authors present a database containing ~400 downstairs models with exactly three MSSM families, one-to-three Higgs pairs, and no exotics, along with the full operator content constrained by the additional U(1) charges, enabling systematic phenomenological studies of proton decay, the $$ term, neutrino masses, and PQ-like symmetries. They also explore geometric aspects of split heterotic geometry, including stability, equivariance, and extensions between line bundles, and report initial results from a large-scale scan on favourable CICYs, finding 202 upstairs GUTs and 407 downstairs models, with further insights into Yukawa structures and potential PQ realizations. The work provides a substantial stepping-stone toward a complete classification and phenomenological assessment of string-derived standard models, highlighting how top-down constraints shape allowed low-energy physics.

Abstract

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 at http://www-thphys.physics.ox.ac.uk/projects/CalabiYau/linebundlemodels/index.html. 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.

Figures (3)

• Figure 1: Example database entry for complete intersection Calabi-Yau three-fold 6732.
• Figure 2: Example database entry specifying basic properties of a line bundle standard model on the three-fold in Fig. \ref{['fig:cicy6732']}.
• Figure 3: Example database entry specifying operators for the line bundle standard model in Fig. \ref{['fig:model7_1']}.