Abstract
Supergravity theories in more than four dimensions with grand unified gauge symmetries are an important intermediate step towards the ultraviolet completion of the Standard Model in string theory. Using toric geometry, we classify and analyze six-dimensional F-theory vacua with gauge group SO(10) taking into account Mordell-Weil U(1) and discrete gauge factors. We determine the full matter spectrum of these models, including charged and neutral SO(10) singlets. Based solely on the geometry, we compute all matter multiplicities and confirm the cancellation of gauge and gravitational anomalies independent of the base space. Particular emphasis is put on symmetry enhancements at the loci of matter fields and to the frequent appearance of superconformal points. They are linked to non-toric Kähler deformations which contribute to the counting of degrees of freedom. We compute the anomaly coefficients for these theories as well by using a base-independent blow-up procedure and superconformal matter transitions. Finally, we identify six-dimensional supergravity models which can yield the Standard Model with high-scale supersymmetry by further compactification to four dimensions in an Abelian flux background.
Highlights
F-theory [1,2,3] provides a fascinating geometric picture of fundamental forces and matter
To the best of our knowledge, at present there is no fully satisfactory F-theory grand unified theories (GUTs) model, which would have to account for symmetry breaking to the standard model gauge group, the matter content of the standard model, doublet-triplet splitting, sufficiently suppressed proton decay, supersymmetry breaking and semi-realistic quark and lepton mass matrices
We show that theories with non-flat fibers are connected to tops that have points in the interior of a face which can often be reached via tensionless string transition from another top with no superconformal points
Summary
F-theory [1,2,3] provides a fascinating geometric picture of fundamental forces and matter. As we are considering resolved SO(10) models, we encounter many theories with superconformal points, present as non-flat fibers in codimension two In this analysis we study these theories, i.e. matter representations, anomaly cancellation and relations to other theories via tensionless string transitions [45] in global F-theory models over an arbitrary base. In our analysis of the 6d F-theory vacua we determine the complete massless matter spectra, including all SO(10) singlets and non-flat fibers points, i.e. SCPs, using geometric computations only. These models contain one charged 16-plet that yields the quark-lepton generations as zero modes in an Abelian flux compactification, and additional uncharged 16-plets needed for B −L breaking. We evaluate its matter spectrum, Yukawa couplings and anomaly coefficients in full detail
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