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Higgs bundles and UV completion in \(F\)-theory. (English) Zbl 1285.81070
Summary: \(F\)-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 \(\mathrm{SU}(5)\) 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, considering models with base \(\mathbb{CP}^3\) or a blow-up thereof as examples. 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.

MSC:
81V22 Unified quantum theories
81V17 Gravitational interaction in quantum theory
81T13 Yang-Mills and other gauge theories in quantum field theory
83E15 Kaluza-Klein and other higher-dimensional theories
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
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