Three-Family Particle Physics Models from Global F-theory Compactifications

TL;DR

This paper constructs globally consistent F-theory models with three chiral generations matching key GUT models, analyzing flux conditions, matter content, and phenomenological implications for particle physics.

Contribution

It presents the first explicit construction of globally consistent G_4-flux in F-theory models with three generations, connecting GUT models to realistic particle physics.

Findings

Models have three chiral generations and Standard Model-like gauge groups.

Constructed G_4-flux satisfies tadpole cancellation and flux quantization.

Analyzed Higgsing processes from GUT models to the Standard Model.

Abstract

We construct four-dimensional, globally consistent F-theory models with three chiral generations, whose gauge group and matter representations coincide with those of the Minimal Supersymmetric Standard Model, the Pati-Salam Model and the Trinification Model. These models result from compactification on toric hypersurface fibrations $X$ with the choice of base $\mathbb{P}^3$. We observe that the F-theory conditions on the $G_4$-flux restrict the number of families to be at least three. We comment on the phenomenology of the models, and for Pati-Salam and Trinification models discuss the Higgsing to the Standard Model. A central point of this work is the construction of globally consistent $G_4$-flux. For this purpose we compute the vertical cohomology $H_V^{(2,2)}(X)$ in each case and solve the conditions imposed by matching the M- and F-theoretical 3D Chern-Simons terms. We explicitly check that the expressions found for the $G_4$-flux allow for a cancelation of D3-brane tadpoles. We also use the integrality of 3D Chern-Simons terms to ensure that our $G_4$-flux solutions are adequately quantized.