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

TL;DR

This paper introduces an intrinsic F-theory approach to G-fluxes that induce chirality, providing a global extension method and a formula for computing chiral spectra, aligning with semi-local and heterotic results.

Contribution

It presents a novel intrinsic description of G-fluxes in F-theory, enabling global flux extension and a unified formula for chiral spectrum computation.

Findings

Chirality computations match semi-local Higgs bundle analysis.

Results agree with heterotic formulae when applicable.

Proposes a quantization rule consistent with dual descriptions.

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.