Abstract
We study correlations between the massless field spectra of F-theory fibrations supporting an SU(5) gauge symmetry extended by Abelian symmetries and the spectra that arise from the group E 8. The adjoint representation of E 8 leads to six different classes of matter spectra upon Higgsing E 8 to SU(5)×U(1) n . Of 27 different smooth F-theory elliptic fibrations constructed in the literature, satisfying certain genericness and flatness criteria, the matter spectrum of only one can be embedded in these six theories, thereby apparently ruling out any connection. We define an extension of the spectrum arising from the adjoint of E 8 by introducing new SU(5)-singlet fields with Abelian charges such that there exists a cubic gauge invariant coupling between any three representations. Higgsing by these new singlets leads to a further 20 classes of spectra, and we find that all the F-theory fibrations can then be embedded in this extended set. These results show that E 8, when extended in this specific way, may still have a role to play in controlling the possible matter spectra in F-theory. We give an explicit geometric example of the presence of the extending singlets and their Higgsing. We discuss some phenomenological applications of the new set of theories, in particular due to the existence of a ℤ2 matter parity. Finally we make some comments on the Heterotic duals of the F-theory fibrations which extend E 8 in this way.
Highlights
We study correlations between the massless field spectra of F-theory fibrations supporting an SU(5) gauge symmetry extended by Abelian symmetries and the spectra that arise from the group E8
Course there remained much data of the theory, such as the massless spectrum and the values of operators, which depends on the precise details of the background geometry and fluxes, but the possible Abelian symmetries for any such model were embeddable inside the group E8 and the possible matter charges under the symmetries were all realised in the decomposition of a single 248 adjoint representation of E8
With the aim of moving towards a more systematic understanding of the set of possibilities for F-theory GUT constructions, we study if there is a similar role that the group E8 can play in constraining the possible symmetries and matter charges in full global F-theory models
Summary
We are interested in models of the type SU(5) × U(1)n, where n ranges between 0 and 4. For SO(10) or larger GUT groups the Abelian charges are such that the matter curves and singlets can always form a complete flat network. The natural conclusion one can reach from these considerations is that F-theory fibrations which form complete flat networks can have more singlet fields than those coming from a single adjoint representation of E8. This observation leads to a natural extension of the spectrum of fields coming from the adjoint of E8 as follows: for each pair of 5 matter curves we impose that there should be a singlet field such that there is a gauge invariant 1 5 ̄5 coupling.
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