Higgs Bundles and UV Completion in F-Theory

By R. Donagi, M. Wijnholt. 2009

214 citations recorded by the source corpus.

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, considering models with base CP3 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/927732573c86f7b174499ae5faee54cf7b91ba4d

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Citations in the corpus

F-theory compactifications with multiple U(1)-factors: constructing elliptic fibrations with rational sections (2013, background): “However, aspects of the physics of U(1)-symmetries can already be studied in local F-theory models employing spectral cover methods [25, 26, 6, 27, 28, 29, 30, 31].”
U(1) symmetries in F-theory GUTs with multiple sections (2012, methodology): “Generally the fibration over SGUT can act with this group which in F-theory is termed monodromies [31, 12].”
F-theory GUT vacua on compact Calabi-Yau fourfolds (2009, methodology): “Motivated by this picture, a convenient way to describe the physics of a GUT model has been developed in [2, 38, 15, 39] in terms of the spectral cover construction [40, 41] over S.”
Global F-theory GUTs (2009, background): “In [26, 27] it was realized that a natural description of certain geometric aspects and the gauge flux is in terms of the spectral cover construction, which first came to stage in string theory in the context of heterotic compactifications [28, 29].”
MODELS OF PARTICLE PHYSICS FROM TYPE IIB STRING THEORY AND F-THEORY: A REVIEW (2012, methodology): “The most direct result is the absence of any net chirality induced by hypercharge flux in the absence of any splitting in the spectral cover [251].”
G-flux in F-theory and algebraic cycles (2011, methodology): “The weak coupling region of the CY fourfold moduli space is reached in the following way: One scales the sections ai as (see [5, 13]) a3 → ǫ a3 a4 → ǫ a4 a6 → ǫ (2)a6 , (5.”
Anomaly equations and intersection theory (2011, background): “Acknowledgement First and foremost I would like to thank Wati Taylor for his guidance, support and en(12)An incomplete list of references on the structure of four-dimensional F-theory backgrounds is given in the bibliography [25, 52, 55, 58, 79, 80, 81, 82, 83, 84].”
Small resolutions of SU(5)-models in F-theory (2011, methodology): “Another approach based on the field theory on the seven-branes world volume has been developed recently [25, 26, 27, 32].”
New aspects of Heterotic–F-theory duality (2008, background): “Since the authors of [53] assigned a scaling dimension r to ar (r = 5, 4, 3, 0), the first three terms have all scaling dimension 9, whereas the last two term have higher dimensions.”
G(4)-flux, chiral matter and singularity resolution in F-theory compactifications (2011, background): “It is interesting to compare the globally defined U(1)X G4-flux with the bundles constructed in the spectral cover approach [6, 52].”
Compact F-theory GUTs with U(1)PQ (2009, methodology): “While there is a topological constraint that must be satisfied globally in order to prevent the U(1)Y gauge boson from becoming massive [5, 6, 23], the most severe constraints at the moment seem to arise from the study of semi-local models [1, 22 ], which focus on the geometry near the 7-branes whe”
T-branes and monodromy (2010, background): “For comparison with previous results studied in the literature, what we have derived is essentially the conditions under which the spectral equation technology used in references [12,18] is applicable.”