Global gluing and G -flux

bstract 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.