G4-Flux and Standard Model Vacua in F-theory

TL;DR

This paper analyzes gauge fluxes in F-theory models with Standard Model-like gauge groups, providing a geometric classification of fluxes, computing matter surface classes, and demonstrating explicit chiral spectrum calculations.

Contribution

It introduces a geometric classification of gauge fluxes in F-theory with Standard Model gauge groups and computes matter surface classes for anomaly cancellation and chiral spectrum determination.

Findings

Derived explicit formulas for matter surface classes.

Achieved anomaly cancellation conditions geometrically.

Found consistent flux configurations with Standard Model spectra.

Abstract

We study the geometry of gauge fluxes in four-dimensional F-theory vacua with gauge group SU(3)xSU(2)xU(1)xU(1) and its implications for phenomenology. The models are defined by a previously introduced class of elliptic fibrations whose fibre is given as a cubic hypersurface in ${\rm Bl}_2{\mathbb P}^2$, with the non-abelian gauge group factors SU(3)xSU(2) engineered torically via the top construction. To describe gauge fluxes on these fibrations we provide a classification of the primary vertical middle cohomology group in a fashion valid for any choice of base space. Using the ideal theoretic technique of primary decomposition we compute the cohomology classes of the matter surfaces associated with states charged under the non-abelian gauge group. These expressions allow us to interpret the cancellation of the pure and mixed non-abelian anomalies geometrically as a result of the general form of the matter surfaces, without reference to a specific type of gauge flux. Explicit results for the chiral indices of all matter states are obtained in terms of intersection numbers of the base and can be directly applied to any choice of base consistent with the fibration. As a demonstration we scan for globally consistent F-theory vacua on $\mathbb P^3$, ${\rm Bl}_1\mathbb P^3$ and ${\rm Bl}_2 \mathbb{P}^3$, and find a globally consistent flux configuration with the chiral Standard Model spectrum plus an extra triplet pair, which may be lifted by a recombination process.