On G-flux, M5 instantons, and U(1)s in F-theory
Joseph Marsano, Natalia Saulina, Sakura Schafer-Nameki
TL;DR
This work develops a global framework for G-flux and U(1) symmetries in F-theory GUTs by extending local Higgs-bundle data to the full Calabi–Yau fourfold through spectral divisors, notably introducing the Tate divisor. It analyzes M5-instantons in the presence of G-flux, detailing fermion zero-mode counting and the (generally) trivial restriction of chirality-inducing flux to M5 worldvolumes, with potential uncharged instanton couplings that can aid Kahler moduli stabilization. An explicit application to a Marsano–Schäfer-Nameki geometry demonstrates how to identify vertical divisors capable of generating nonzero instanton superpotential contributions, while ensuring compatibility with fluxes that generate chirality. The results provide a path toward globally consistent F-theory GUT completions, including a careful treatment of D3-tadpole, flux quantization, and potential charged couplings via M2-branes. Overall, the paper offers a concrete, geometrically grounded method to incorporate G-flux, U(1)s, and M5-instantons into global F-theory models with implications for moduli stabilization and phenomenology.
Abstract
Local aspects of singular F-theory compactifications for SUSY GUT model-building are fairly well understood in terms of Higgs bundles and their spectral data. Several global issues remain, however, including a description of G-fluxes, which are key to constructing chiral matter and stabilizing moduli, and the global realization of U(1) symmetries that can forbid phenomenologically unfavorable couplings. In this paper, we sharpen our earlier proposal for describing G-fluxes through "spectral divisors" and introduce a distinguished "Tate divisor", which can be used to describe both G-flux and U(1)s when present. As an application, we give a general discussion of M5-instanton contributions in the presence of G-flux and exemplify this in a concrete example, where we comment on the ability of instanton induced superpotential couplings to stabilize Kahler moduli.