General U(1)×U(1) F-theory compactifications and beyond: geometry of unHiggsings and novel matter structure
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Author(s)
Cvetič, Mirjam
Klevers, Denis
Piragua, Hernan
Taylor IV, Washington
Date Issued
November 2015
Journal
Journal of High Energy Physics
Publisher
Springer Berlin Heidelberg
Citation
Cvetič, Mirjam et al. “General U(1)×U(1) F-Theory Compactifications and beyond: Geometry of unHiggsings and Novel Matter Structure.” Journal of High Energy Physics 2015.11 (2015): n. pag.
Version
Final published version
Abstract
We construct the general form of an F-theory compactification with two U(1) factors based on a general elliptically fibered Calabi-Yau manifold with Mordell-Weil group of rank two. This construction produces broad classes of models with diverse matter spectra, including many that are not realized in earlier F-theory constructions with U(1)×U(1) gauge symmetry. Generic U(1)×U(1) models can be related to a Higgsed non-Abelian model with gauge group SU(2)×SU(2)×SU(3), SU(2)[superscript 3]×SU(3), or a subgroup thereof. The nonlocal horizontal divisors of the Mordell-Weil group are replaced with local vertical divisors associated with the Cartan generators of non-Abelian gauge groups from Kodaira singularities. We give a global resolution of codimension two singularities of the Abelian model; we identify the full anomaly free matter content, and match it to the unHiggsed non-Abelian model. The non-Abelian Weierstrass model exhibits a new algebraic description of the singularities in the fibration that results in the first explicit construction of matter in the symmetric representation of SU(3). This matter is realized on double point singularities of the discriminant locus. The construction suggests a generalization to U(1)[superscript k] factors with k > 2, which can be studied by Higgsing theories with larger non-Abelian gauge groups.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1007/JHEP11(2015)204
