Abstract:
We study the minimal supersymmetric standard model derived from the $Z_8$ orbifold models and its hidden sectors. We use a target-space duality anomaly cancellation so as to investigate hidden sectors consistent with the MSSM unification. For the allowed hidden sectors, we estimate the running gauge coupling constants making use of threshold corrections due to the higher massive modes. The calculation is important from the viewpoint of gaugino condensations, which is one of the most promissing mechanism to break the supersymmetry.

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 U(1)$_Y$ and examine consistencies of the model with the LEP experiments. It is found that $Z_4$ and $Z_8$-II can not derive the minimal string model but $Z_6$-I, $Z_6$-II and $Z_8$-I are possible to derive it with $13/12 \leq k_1\leq 41/30$, $16/15\leq k_1\leq 17/12$ and $1\leq k_1\leq 41/21$ respectively. The minimum values of the moduli on unrotated planes are estimated within the ranges of the levels.

Abstract:
We study the minimal supersymmetric standard model derived from $Z_N \times Z_M$ orbifold models. Moduli dependent threshold corrections of the gauge couplings are investigated to explain the measured values of the coupling constants. Also we study Yukawa couplings of the models. We find that the $Z_2 \times Z_6'$, $Z_2\times Z_6$, $Z_3 \times Z_6$ and $Z_6 \times Z_6$ orbifold models have the possibility to derive Yukawa couplings for the second and third generations as well as the measured gauge coupling constants. Allowed models are shown explicitly by combinations of modular weights for the matter fields.

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 U(1)$_Y$ and examine consistencies of the model with the LEP experiments. 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.

Abstract:
Some results are presented concerning duality invariant effective string actions and the construction of automorphic functions for general (2,2) string compactifications. These considerations are applied in order to discuss the {\it minimal} unification of gauge coupling constants in orbifold compactifications with special emphasis on string threshold corrections.

Abstract:
We consider the sparticle and higgs spectroscopy in a class of superstring inspired models in which the string threshold corrections ensure the consistency of the string unification scale with the low energy data. The lightest neutralino is almost a pure bino and it is predicted to be the lightest sparticle (LSP). Requiring that $\Omega_{LSP}\leq 0.9$, we find an upper bound on its mass which, in the case of dilaton supersymmetry breaking, turns out to be 160 GeV. The LEP 1.5 experimental lower bound on the chargino mass, $m_{\chi^{\pm}} > 65$ GeV, implies that the lower bound on the LSP mass is $m_{LSP} > 32 (45)$ GeV, corresponding to $\mu < (>)0$. We also determine the lower and upper bounds on the higgs and other sparticle masses. For instance, the lightest higgs lies between 65 and 115 GeV, while the mass of the lightest charged sparticle satisfies 47 GeV $ < m_{\tilde{e}_R} < 325$ GeV. With only the top Yukawa coupling of order unity we find that $ 1.5 \leq \tan \beta \leq 3.5$.

Abstract:
The significant heavy threshold effect is found in the supersymmetric SU(5) model with two adjoint scalars, one of which is interpreted as a massive string mode decoupled from the lower-energy particle spectra. This threshold related with the generic mass splitting of the basic adjoint moduli is shown to alter properly the running of gauge couplings, thus giving a natural solution to the string-scale grand unification as prescribed at low energies by LEP precision measurements and minimal particle content. The further symmetry condition of the (top-bottom) Yukawa and gauge coupling superunification at a string scale results in the perfectly working predictions for the top and bottom quark masses in the absence of any large supersymmetric threshold corrections.

Abstract:
We exploit the measured branching ratio for $b \rightarrow s\gamma$ to derive lower limits on the sparticle and Higgs masses in the minimal string unification models. For the LSP('bino'), chargino and the lightest Higgs, these turn out to be 50, 90 and 75 GeV respectively. Taking account of the upper bounds on the mass spectrum from the LSP relic abundance, we estimate the direct detection rate for the latter to vary from 10^{-1} to 10^{-4} events/kg/day. The muon flux, produced by neutrinos from the annihilating LSP's, varies in the range 10^{-2} - 10^{-9} muons/m^2/day.

Abstract:
We study the unification scale and gauge coupling constant in 4D string theory. We show that the fine structure constant is determined by the dimension of the hidden gauge group and only $SU(6)$ and $SO(9)$ are consistent with minimal string unification while the unification scale can be of order of $10^{16}\,GeV$.

Abstract:
We provide what we believe is the minimal three family ${\cal N} = 1$ SUSY and conformal Pati-Salam Model from type IIB superstring theory. This $Z_3$ orbifolded AdS$\otimes S^5$ model has long lived protons and has potential phenomenological consequences for LHC.