Higgs Bundles and UV Completion in F-Theory

TL;DR

This paper develops a rigorous mathematical framework for local F-theory models using Higgs bundles, proves a no-go theorem for certain GUT models, and explores conditions for realistic global models with suppressed proton decay.

Contribution

It introduces an intrinsic construction of local F-theory models via spectral covers and proves the non-existence of certain three-generation SU(5) models for generic moduli.

Findings

Local models are described by meromorphic Higgs bundles with spectral cover.

No-go theorem shows three-generation SU(5) models do not exist for generic moduli.

Global models can be constructed with fluxes that suppress proton decay.

Abstract

F-theory admits 7-branes with exceptional gauge symmetries, which can be compactified to give phenomenological four-dimensional GUT models. Here we study general supersymmetric compactifications of eight-dimensional Yang-Mills theory. They are mathematically described by meromorphic Higgs bundles, and therefore admit a spectral cover description. This allows us to give a rigorous and intrinsic construction of local models in F-theory. We use our results to prove a no-go theorem showing that local SU(5) models with three generations do not exist for generic moduli. However we show that three-generation models do exist on the Noether-Lefschetz locus. We explain how F-theory models can be mapped to non-perturbative orientifold models using a scaling limit proposed by Sen. Further we address the construction of global models that do not have heterotic duals. We show how one may obtain a contractible worldvolume with a two-cycle not inherited from the bulk, a necessary condition for implementing GUT breaking using fluxes. We also show that the complex structure moduli in global models can be arranged so that no dimension four or five proton decay can be generated.