Abstract:
The supersymmetry breaking parameters and the resulting supersymmetric particle spectrum are studied in orbifold compactifications of string theory under the assumption that unification of gauge coupling constants at about $10^{16}$ GeV is a consequence of large moduli dependent string loop threshold corrections. The effect on the spectrum of various assumptions as to the modular weights of the states, the values of the Green-Schwarz parameter, $\delta_{GS}$, the origin of the $\mu$ parameter and the moduli dependence of Yukawa couplings is discussed. The effect of radiative corrections to the effective potential is also considered.

Abstract:
We discuss how unification of the gauge, Higgs and (three chiral family) matter superfields can be realized from the compactification of a six dimensional supersymmetric SU(8) gauge theory over the orbifold R^4 x T^2/Z_3. The bulk gauge interaction includes Yukawa interactions to generate masses for quarks and leptons after the electroweak symmetry is broken. The Yukawa matrices in this case turn out to be antisymmetric, and thus not phenomenologically viable. To overcome this we introduce brane fields which are vector-like under the standard model gauge symmetry, and so do not alter the number of chiral families. In such a setup, the observed fermion masses and mixings can be realized by taking into account suppression effects from the effective Wilson line couplings and large volume of the extra dimensions.

Abstract:
A natural gradual extension of the idea of Grand Unification is to attempt to relate the gauge and Yukawa couplings; Gauge-Yukawa Unification (GYU). However, within the framework of renormalizable field theories, there exists no realistic symmetry that leads to a GYU. Here we propose an approach to GYU which is based on the principle of the reduction of couplings and finiteness in supersymmetric Grand Unified Theories. We elucidate how the observed top-bottom mass hierarchy can be explained in terms of supersymmetric GYU by considering an example of the $SU(5)$ Finite Unified Theory. It is expected that, when more accurate measurements of the top and bottom quark masses are available, it will be possible to discriminate among the various GYU models.

Abstract:
We investigate the effects of Yukawa couplings on the phenomenological predictions for a class of supersymmetric models which allows for the presence of complete SU(5) multiplets in addition to the Minimal Supersymmetric Standard Model spectrum. We develop a two loop analytical approach to quantify the predictions for gauge unification including Yukawa couplings. The effects of the heavy thresholds of the model are also included. In some cases accurate predictions can be made for the unification scale, irrespective of the initial (unknown) Yukawa couplings, so long as perturbation theory remains valid. We also consider the limit of a large number of extra states and compute the predictions in a resummed perturbation series approach to show that the results are stable in this limit. Finally we consider the possibility of making predictions for the case the gauge and Yukawa couplings enter the non-perturbative domain below the unification scale and estimate the errors which affect these predictions.

Abstract:
The unification of gauge and Yukawa couplings within the minimal supersymmetric standard model is studied at the two loop level. We derive an expression for the effective scale, $T_{SUSY}$, which characterizes the supersymmetric particle threshold corrections to the gauge couplings, and demonstrate that $T_{SUSY}$ is only slightly dependent on the squark and slepton masses, and strongly dependent on the Higgsino masses as well as on the mass ratio of the gauginos of the strong and weak interactions. Moreover, the value of the top quark Yukawa coupling necessary to achieve the unification of bottom and tau Yukawa couplings is also governed by $T_{SUSY}$, and it yields predictions for the top quark mass which are close to the quasi infrared fixed point results associated with the triviality bounds on this quantity. From the requirement of perturbative consistency of the top quark Yukawa sector of the theory, we obtain constraints on the allowed splitting of the supersymmetric spectrum, which, for certain values of the running bottom quark mass, are stronger than those ones coming from the experimental constraints on the strong gauge coupling.

Abstract:
We present analytic expressions for the top and bottom Yukawa couplings in the context of the minimal supersymmetric standard model when both couplings $h_{t,0},h_{b,0}$ are large at the unification scale. For sufficiently large $h_{t,0},h_{b,0}$, i.e. within $\sim (20-25)\% $ close to their fixed point values, using as input the central value of the bottom mass $m_b(m_b)=4.25GeV$, we find that the top mass lies in the range $m_t \approx (174-178)GeV$, while $tan\beta \approx (55-58)$. Implications on the evolution of the scalar masses and the radiative symmetry breaking scenario are discussed. %

Abstract:
The wave functions and Yukawa couplings of the top and bottom quarks in the SO(5) x U(1) gauge-Higgs unification model are determined. The result is summarized in the effective interactions for \hat \theta_H(x) = \theta_H + H(x)/f_H where \theta_H is the Wilson line phase and H(x) is the 4D Higgs field. The Yukawa, WWH and ZZH couplings vanish at \theta_H = \onehalf \pi. There emerges the possibility that the Higgs particle becomes stable.

Abstract:
The consequences of assuming the third-generation Yukawa couplings are all large and comparable are studied in the context of the minimal supersymmetric extension of the standard model. General aspects of the RG evolution of the parameters, theoretical constraints needed to ensure proper electroweak symmetry breaking, and experimental and cosmological bounds on low-energy parameters are presented. We also present complete and exact semi-analytic solutions to the 1-loop RG equations. Focusing on SU(5) or SO(10) unification, we analyze the relationship between the top and bottom masses and the superspectrum, and the phenomenological implications of the GUT conditions on scalar masses. Future experimental measurements of the superspectrum and of the strong coupling will distinguish between various GUT-scale scenarios. And if present experimental knowledge is to be accounted for most naturally, a particular set of predictions is singled out.

Abstract:
We study the construction of the minimal supersymmetric standard model from the $Z_8$ orbifold models. We use a target-space duality anomaly cancellation and a unification of gauge couplings as constraints. It is shown that some models obtained through a systematical search realize the unification of SU(3) and SU(2) coupling constants.