Global Gluing and G-flux

TL;DR

Global Gluing and G-flux shows that local F-theory GUT data, encoded in a Higgs-bundle spectral cover, is completed by global information carried by a spectral divisor ${\cal C}_F$ and a line bundle ${\cal N}_F$ on it. Restricting ${\cal N}_F$ to the local spectral data ${\cal C}_{loc}$ yields the local flux and the gluing data, fixing the full local model in a way that agrees with heterotic duals when available. The authors demonstrate, via an explicit example, that gluing can shift the detailed spectrum (e.g., changing the $f\overline{10}$ count) without altering net chirality, and they discuss how splits of ${\cal C}_F$ signal extra $U(1)$ factors or larger gauge groups, with implications for a global 3-form potential $C_3$. Overall, the work provides a concrete, globally defined mechanism to determine gluing in local F-theory constructions, ensuring consistent chirality and spectrum across local-global realizations.

Abstract

Local models that capture the 7-brane physics of F-theory compactifications for supersymmetric GUTs are conveniently described in terms of an E_8 gauge theory in the presence of a Higgs bundle. Though the Higgs bundle data is usually determined by the local geometry and G-flux, additional gluing data must be specified whenever the Higgs bundle spectral cover is not smooth. In this paper, we argue that this additional information is determined by data of the M-theory 3-form that is not necessarily captured by the cohomology class of the G-flux. More specifically, we show that when the 3-form is specified in terms of a line bundle on a spectral divisor, which is a global extension of the Higgs bundle spectral cover, the gluing data of the local model is uniquely determined in a way that ensures agreement with Heterotic results whenever a Heterotic dual exists.