Soft Supersymmetry-breaking terms and the \mu problem

The connection between Supergravity and the low-energy world is analyzed. In particular, the soft Supersymmetry-breaking terms arising in Supergravity, the $\mu$ problem and various solutions proposed to solve it are reviewed. The soft terms arising in Supergravity theories coming from Superstring theory are also computed and the solutions proposed to solve the $\mu$ problem, which are naturally present in Superstrings, are also discussed. The $B$ soft terms associated are given for the different solutions. Finally, the low-energy Supersymmetric-spectra, which are very characteristic, are obtained.Comment: Based on talks given at different Conferences, 33 pages, late

Optical Unification

We discuss string scale unification facilitated by exotic matter with masses at intermediate scales, between the observable sector supersymmetry breaking scale and the string scale. We point out a mechanism by which string scale unification may occur while producing a (lower) virtual unification scale independent of the location of the intermediate scale and the value of the string coupling. The apparent unification obtained by extrapolating low energy gauge couplings is not accidental when this mechanism is invoked; virtual unification is robust.Comment: 9 pages, references adde

Soft supersymmetry-breaking terms from supergravity and superstring models

We review the origin of soft supersymmetry-breaking terms in N=1 supergravity models of particle physics. We first consider general formulae for those terms in general models with a hidden sector breaking supersymmetry at an intermediate energy scale. The results for some simple models are given. We then consider the results obtained in some simple superstring models in which particular assumptions about the origin of supersymmetry breaking are made. These are models in which the seed of supersymmetry breaking is assumed to be originated in the dilaton/moduli sector of the theory.Comment: 24 pages, to appear in the book `Perspectives on Supersymmetry', World Scientific, Editor G. Kane; some comments and references adde

Complete structure of Z_n Yukawa couplings

We give the complete twisted Yukawa couplings for all the Z_n orbifold constructions in the most general case, i.e. when orbifold deformations are considered. This includes a certain number of tasks. Namely, determination of the allowed couplings, calculation of the explicit dependence of the Yukawa couplings values on the moduli expectation values (i.e. the parameters determining the size and shape of the compactified space), etc. The final expressions are completely explicit, which allows a counting of the DIFFERENT Yukawa couplings for each orbifold (with and without deformations). This knowledge is crucial to determine the phenomenological viability of the different schemes, since it is directly related to the fermion mass hierarchy. Other facts concerning the phenomenological profile of Z_n orbifolds are also discussed, e.g. the existence of non--diagonal entries in the fermion mass matrices, which is related to a non--trivial structure of the Kobayashi--Maskawa matrix. Finally some theoretical results are given, e.g. the no--participation of (1,2) moduli in twisted Yukawa couplings. Likewise, (1,1) moduli associated with fixed tori which are involved in the Yukawa coupling, do not affect the value of the coupling.Comment: 60 page