A Note on G-Fluxes for F-theory Model Building

TL;DR

This work develops an intrinsic F-theory framework for G-fluxes that induce chirality, avoiding reliance on heterotic duals by introducing a spectral divisor ${\cal C}$ and a traceless twist $\gamma$ to define supersymmetric, Lorentz-invariant fluxes. It then derives a general chirality formula that expresses net chiral indices as integrals of $\gamma$ over dual matter surfaces, and demonstrates agreement with heterotic/Higgs-bundle results in dual or local limits. The approach extends semi-local fluxes to global models, clarifies monodromy and $U(1)$ symmetries via spectral-divisor factorization, and provides a quantization rule aligned with $SU(5)_{\perp}$ bundle data. The framework is then applied to connect semi-local constructions to globally embedded Calabi-Yau fourfolds, including 3+2 factorizations and charged singlets, offering a practical route for global F-theory GUT model building and flux counting. Overall, the paper provides a self-contained, duality-consistent method to compute chiral spectra in globally-embedded F-theory GUTs and to study the role of monodromy and $U(1)$ symmetries in fluxed compactifications.

Abstract

We propose a description of G-fluxes that induce chirality in 4-dimensional F-theory GUT spectra that is intrinsic to F-theory and does not rely on Heterotic/F-theory duality. Using this, we describe how to globally extend fluxes that have been constructed in a semi-local setting and obtain an F-theoretic formula for computing the chiral spectrum that they induce. Chirality computations agree with those from the semi-local Higgs bundle analysis for matter fields that are charged under the GUT-group, and hence with the standard Heterotic formulae where applicable. Finally, the relation of G-fluxes to SU(5)_{perp} bundles on the F-theory 4-fold is discussed and used to motivate a quantization rule that is consistent both with the Higgs bundle one as well as the Heterotic one when a Heterotic dual exists.