Towards the Standard Model spectrum from elliptic Calabi-Yau

TL;DR

This paper demonstrates the construction of supersymmetric three-generation Standard Model-like theories using elliptically fibered Calabi-Yau manifolds with bi-sections, expanding the geometric framework for string phenomenology.

Contribution

It introduces a novel approach to building Standard Model spectra from non-simply-connected elliptic Calabi-Yau manifolds with bi-sections, including explicit examples with free involutions.

Findings

Constructed models with three generations and Standard Model gauge group

Presented explicit examples using fiber products and Hirzebruch surfaces

Achieved the necessary chiral matter through bundle parameters related to singularities

Abstract

We show that it is possible to construct supersymmetric three-generation models of Standard Model gauge group in the framework of non-simply-connected elliptically fibered Calabi-Yau, without section but with a bi-section. The fibrations on a cover Calabi-Yau, where the model has 6 generations of SU(5) and the bundle is given via the spectral cover description, use a different description of the elliptic fibre which leads to more than one global section. We present two examples of a possible cover Calabi-Yau with a free involution: one is a fibre product of rational elliptic surfaces $dP_9$; another example is an elliptic fibration over a Hirzebruch surface. There we give the necessary amount of chiral matter by turning on in the bundles a further parameter, related to singularities of the fibration and the branching of the spectral cover.