Flipped and unflipped SU(5)SU(5) as type IIA flux vacua

On type IIA orientifolds with flux compactifications in supersymmetric AdS vacua, we for the first time construct SU(5)SU(5) models with three anti-symmetric 10 representations and without symmetric 15 representations. We show that all the pairs of the anti-fundamental 5¯ and fundamental 5 representations can obtain GUT/string-scale vector-like masses after the additional gauge symmetry breaking via supersymmetry preserving Higgs mechanism. Then we have exact three 5¯, and no other chiral exotic particles that are charged under SU(5)SU(5) due to the non-Abelian anomaly free condition. Moreover, we can break the SU(5)SU(5) gauge symmetry down to the SM gauge symmetry via D6-brane splitting, and solve the doublet–triplet splitting problem. Assuming that the extra one (or several) pair(s) of Higgs doublets and adjoint particles obtain GUT/string-scale masses via high-dimensional operators, we only have the MSSM in the observable sector below the GUT scale. Then the observed low energy gauge couplings can be generated via RGE running if we choose the suitable grand unified gauge coupling by adjusting the string scale. Furthermore, we construct the first flipped SU(5)SU(5) model with exact three 10, and the first flipped SU(5)SU(5) model in which all the Yukawa couplings are allowed by the global U(1)U(1) symmetries.