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 Z 2 matter parity. Finally we make some comments on the Heterotic duals of the F-theory fibrations which extend E 8 in this way.

Abstract:We analyse global aspects of 7-brane backgrounds with a non-commuting profile for their worldvolume scalars, also known as T-branes. In particular, we consider configurations with no poles and globally well-defined over a compact Kähler surface. We find that such T-branes cannot be constructed on surfaces of positive or vanishing Ricci curvature. For the existing T-branes, we discuss their stability as we move in Kähler moduli space at large volume and provide examples of T-branes splitting into non-mutuallysupersymmetric constituents as they cross a stability wall.

Abstract:We study α'-corrections in multiple D7-brane configurations with noncommuting profiles for their transverse position fields. We focus on T-brane systems, crucial in F-theory GUT model building. There α -corrections modify the D-term piece of the BPS equations which, already at leading order, require a non-primitive Abelian worldvolume flux background. We find that α -corrections may either i) leave this flux background invariant, ii) modify the Abelian non-primitive flux profile, or iii) deform it to a non-Abelian profile. The last case typically occurs when primitive fluxes, a necessary ingredient to build 4d chiral models, are added to the system. We illustrate these three cases by solving the α -corrected D-term equations in explicit examples, and describe their appearance in more general T-brane backgrounds. Finally, we discuss implications of our findings for F-theory GUT local models.