Global SO(10) F-theory GUTs

TL;DR

The paper develops a framework for global SO$(10)$ F-theory GUTs using toric complete-intersection Calabi–Yau fourfolds built over base manifolds obtained from blowing up Fano threefolds. It implements a split SU$(4)$ spectral cover to generate chiral matter on the ${f 16}$ and ${f 10}$ curves and uses abelian flux $F_X$ to break SO$(10)$ to SU$(5) imes U(1)_X$, interpreted as a flipped SU$(5)$ setup with further breaking to the MSSM. It provides explicit geometric backgrounds (five models) and multiple GUT realizations, including several three- and four-generation examples, along with a detailed phenomenological analysis of the resulting spectra and Yukawa couplings. The work also discusses Euler-number computations, tadpole constraints, and potential mismatches between toric and formula-based predictions, highlighting areas for further refinement and moduli stabilization in global F-theory GUTs.

Abstract

Making use of toric geometry we construct a class of global F-theory GUT models. The base manifolds are blowups of Fano threefolds and the Calabi-Yau fourfold is a complete intersection of two hypersurfaces. We identify possible GUT divisors and construct SO(10) models on them using the spectral cover construction. We use a split spectral cover to generate chiral matter on the 10 curves in order to get more degrees of freedom in phenomenology. We use abelian flux to break SO(10) to SU(5)\times U(1) which is interpreted as a flipped SU(5) model. With the GUT Higgses in the SU(5)\times U(1) model it is possible to further break the gauge symmetry to the Standard Model. We present several phenomenologically attractive examples in detail.