Global Gluing and G-flux

TL;DR

This paper explores how additional gluing data in F-theory local models, related to G-flux and the M-theory 3-form, can be globally determined via spectral divisors, ensuring consistency with Heterotic duals.

Contribution

It introduces a method to determine gluing data from the M-theory 3-form using spectral divisors, linking local F-theory models to global geometric data.

Findings

Gluing data is determined by the M-theory 3-form on spectral divisors.

Ensures compatibility of local models with global F-theory compactifications.

Matches Heterotic dual results when applicable.

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.