Minimal string unification and constraint on hidden sector

Abstract

We examine whether a minimal string model possessing the same massless spectra as the MSSM can be obtained from Z 4, Z 6 and Z 8 orbifold constructions. Using an anomaly cancellation condition of the target space duality symmetry, we derive allowable values of a level k 1 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 Z 4 and Z 8-II cannot derive the minimal string model but Z 6-I, Z 6-II and Z 8-I are possible to derive it with k 1 = 29/21, 1 ⩽ k 1 ⩽ 32/21 and 1 ⩽ k 1 ⩽ 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.