Minimal string unification and constraint on hidden sector Original Research Article

We examine whether a minimal string model possessing the same massless spectra as the MSSM can be obtained from Z4, Z6 and Z8 orbifold constructions. Using an anomaly cancellation condition of the target space duality symmetry, we derive allowable values of a level k1 of U(1)Y for the minimal string model on the orbifolds through computer analyses. We investigate threshold corrections of the gauge coupling constants of SU(3), SU(2) and UU(1)Y and examine consistencies of the model with the LEP experiments. It is found that Z4 and Z8-II cannot derive the minimal string model but Z6-I, Z6-II and Z8-I are possible to derive it with k1 = 29/21, 1 ⩽ k1 ⩽ 32/21 and 1 ⩽ k1 ⩽ 41/21, respectively. We obtain explicitly allowed combinations of modular weights. The minimum values of the moduli on unrotated planes are estimated within the ranges of the levels. Further we investigate what kinds of hidden sectors are consistent with the minimal string models. Also their gauge coupling constants of the hidden groups are estimated. We discuss Yukawa couplings of the models.