Chiral spectrum of the universal tuned $(\text{SU}(3) \times \text{SU}(2) \times \text{U}(1))/\mathbb{Z}_{6}$ 4D F-theory model

TL;DR

This paper analyzes the chiral matter spectrum in a universal F-theory model with Standard Model-like gauge symmetry, demonstrating that vertical fluxes can produce realistic chiral matter multiplicities consistent with anomaly cancellation.

Contribution

It applies new methods to compute flux backgrounds and chiral spectra in a broad class of F-theory vacua with Standard Model gauge symmetry.

Findings

Vertical fluxes can generate all chiral matter families satisfying anomaly cancellation.

The analysis includes the chiral families of the Minimal Supersymmetric Standard Model.

The model is realized as a cubic in  fibered over a smooth threefold base.

Abstract

We use the recently developed methods of 2108.07810 to analyze vertical flux backgrounds and associated chiral matter spectra in the 4D universal $(\text{SU}(3) \times \text{SU}(2) \times \text{U}(1))/\mathbb{Z}_{6}$ model introduced in 1912.10991, which is believed to describe the most general generic family of F-theory vacua with tuned $(\text{SU}(3) \times \text{SU}(2) \times \text{U(}1))/\mathbb{Z}_{6}$ gauge symmetry. Our analysis focuses on a resolution of a particular presentation of the $(\text{SU}(3) \times \text{SU}(2) \times \text{U}(1))/\mathbb{Z}_{6}$ model in which the elliptic fiber is realized as a cubic in $\mathbb{P}^2$ fibered over an arbitrary smooth threefold base. We show that vertical fluxes can produce nonzero multiplicities for all chiral matter families that satisfy 4D anomaly cancellation, which include as a special case the chiral matter families of the Minimal Supersymmetric Standard Model.