MSSM from F-theory SU(5) with Klein monodromy

Abstract

We revisit a class of $SU(5)$ supersymmetric grand unified theory (SUSY GUT) models which arise in the context of the spectral cover with Klein Group monodromy ${V}_{4}={Z}_{2}\ifmmode\times\else\texttimes\fi{}{Z}_{2}$. We examine the polynomials of the corresponding factorized spectral cover and discuss the constraints imposed on their coefficients for the transitive and nontransitive realization of this monodromy. We show that ${Z}_{2}$ matter parities can be realized via new geometric symmetries respected by the spectral cover.