On E 8 and F-theory GUTs

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

Discrete gauge symmetries by Higgsing in four-dimensional F-theory compactifications

We study F-theory compactifications to four dimensions that exhibit discrete gauge symmetries. Geometrically these arise by deforming elliptic fibrations with two sections to a genus-one fibration with a bi-section. From a four-dimensional field theory perspective they are remnant symmetries from a Higgsed U(1) gauge symmetry. We implement such symmetries in the presence of an additional SU(5) symmetry and associated matter fields, giving a geometric prescription for calculating the induced discrete charge for the matter curves and showing the absence of Yukawa couplings that are forbidden by this charge. We present a detailed map between the field theory and the geometry, including an identification of the Higgs field and the massless states before and after the Higgsing. Finally we show that the Higgsing of the U(1) induces a G-flux which precisely accounts for the change in the Calabi-Yau Euler number so as to leave the D3 tadpole invariant

M-theory compactifications to three dimensions with M2-brane potentials

We study a class of compactifications of M-theory to three dimensions that preserve N = 2 supersymmetry and which have the defining feature that a probe space-time filling M2 brane feels a non-trivial potential on the internal manifold. Using M-theory/F-theory duality such compactifications include the uplifts of 4-dimensional N = 1 type IIB compactifications with D3 potentials to strong coupling. We study the most general 8-dimensional manifolds supporting these properties, derive the most general flux that induces an M2 potential, and show that it is parameterised in terms of two real vectors. We study the supersymmetry equations when only this flux is present and show that over the locus where the M2 potential is non-vanishing the background takes the form of a Calabi-Yau three-fold fibered over a 2-dimensional base spanned by the flux vectors, while at the minima of the potential the flux vanishes. Allowing also for non-vanishing four-form flux with one leg in the internal directions we find that the Calabi-Yau three-fold in the fibration is replaced by an SU(3)-structure manifold with torsion classes satisfying 2 W 4 = − W 5