Towards the Standard Model Spectrum From Elliptic Calabi–yau Manifolds

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.

Vector bundle extensions, sheaf cohomology, and the heterotic standard model

“…Until now, the standard way to construct such bundles was to use spectral covers on elliptically fibered threefolds, see [46,47,48]. However, it turned out to be difficult to construct realistic matter spectra in this context, see [49,50,48,51,52,53]. Mixing spectral covers with vector bundle extensions was attempted in [54] for SU(5) bundles, but failed to yield a phenomenologically viable model.…”

Realistic three-generation models from SO(32) heterotic string theory

“…Furthermore, there are much progresses on the resolved toroidal orbifold in [5] and on more general Calabi-Yau manifolds for E 8 ×E 8 and/or SO(32) heterotic string theory via the spectral cover construction [6,7] and the extension of it [8] (see e.g., refs. [9][10][11][12]). 1 In this paper, we study SO (32) heterotic string theory on six-dimensional (6D) torus with magnetic fluxes, which is one of the simplest compactifications leading to a chiral theory.…”

“…[2].) This is because E 8 gauge group involves several candidates of the grand unified groups such as E 6 , SO (10) and SU(5) as the subgroups of E 8 and the E 8 adjoint representation includes matter representations such as 27 of E 6 , 16 of SO(10) and 10 and5 of SU (5). However, in SO(32) heterotic string theory, for example, the 16 spinor representation of SO (10) is not involved in the adjoint representation of SO (32).…”

Heterotic models without fivebranes

“…The existence of τ is related to the existence of a second section of the elliptic fibration [11], [12], [13], [14], [15], [16], [17], [18].…”