On $E_8$ and F-Theory GUTs

Understand

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 $SU(5)\times U(1)^n$.
• 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.