Right-handed neutrinos and U(1)X symmetry-breaking

Abstract

In [1] we proposed a model for Heterotic F-theory duality with Wilson line symmetry-breaking and a 4 + 1 split of the F-theory spectral divisor. One goal of this note is to call attention to the existence of right-handed neutrinos in our F-theory model. As pointed out in section 4 of [2] such existence may be evidence for the U(1)X-symmetry that remains after the Higgsing of E8 via E8 ⇒ SU(5)gauge ⊕ [SU(4) ⊕ U(1)X]Higgs occasioned by the 4 + 1 split of the spectral divisor. In addition, as a result of the ℤ2-action that supports the Wilson line we argue that the U(1)X-symmetry is, in fact, broken to ℤ2-matter parity. Finally we identify co-dimension 3 singularities which determine Yukawa couplings for the MSSM matter fields.