We extend the KKLT [1] approach to moduli stabilization by including the dilaton and the complex structure moduli into the effective supergravity theory. Decoupling of the dilaton is neither always possible nor necessary for the existence of stable minima with zero (or positive) cosmological constant. The pattern of supersymmetry breaking can be much richer than in the decoupling scenario of KKLT.

The condition of unification of gauge couplings in the minimal supersymmetric standard model provides successful predictions for the weak mixing angle as a function of the strong gauge coupling and the supersymmetric threshold scale. In addition, in some scenarios, e.g. in the minimal SO(10) model, the tau lepton and the bottom and top quark Yukawa couplings unify at the grand unification scale. The condition of Yukawa unification leads naturally to large values of tan β, implying a proper top quark-bottom quark mass hierarchy. In this work, we investigate the feasibility of unification of the Yukawa couplings, in the framework of the minimal supersymmetric standard model with (assumed) universal mass parameters at the unification scale and with radiative breaking of the electroweak symmetry. We show that strong correlations between the parameters µ 0 , M 1/2 and δ = B 0 − (6r/7)A 0 appear within this scheme, where r is the ratio of the top quark Yukawa coupling to its infrared fixed point value. These correlations have relevant implications for the sparticle spectrum, which presents several characteristic features. In addition, we show that due to large corrections to the running bottom quark mass induced through the supersymmetry breaking sector of the theory, the predicted top quark mass and tan β values are significantly lower than those previously estimated in the literature. Recently, it has been observed that for the phenomenologically allowed values of the bottom quark mass and moderate values of tan β < 10, large values of the top quark Yukawa coupling are needed in order to contravene the strong gauge coupling renormalization of the bottom Yukawa coupling [7]-[9]. In general, for large enough values of the top quark Yukawa coupling at the grand unification scale, the low energy Yukawa coupling is strongly focussed to a quasi infrared fixed point [10]-[11]. In the minimal supersymmetric standard model, the quasi infared fixed point predictions for the physical top quark mass M t are given by M t ≃ A sin β, with A ≃ 190 − 210 GeV for the strong gauge coupling α 3 (M Z ) = 0.11−0.13. It has been recently shown that for the values of the strong gauge coupling consistent with the condition of gauge coupling unification, with reasonable threshold corrections at the grand unification and supersymmetry breaking scales, the top quark mass should be within 10% of its quasi infrared fixed point values if the condition of bottom-tau Yukawa unification is required [12]. A more predictive scheme is obtained in the framework of the minimal SO(10) unification. In this case top-bottom quark Yukawa unification is also required, implying that, for a given value of the bottom quark mass and the strong gauge coupling value [13], not only the top quark mass but also the value of tan β may be determined. Remarkably, large values of tan β ≥ 40 are obtained in this case, leading to a proper bottom-top mass hierarchy [14]-[16]. For these large values of tan β, the bottom quark Yukawa coupling itself plays a relevant role in the ...

We examine the structure of soft supersymmetry breaking terms in KKLT models of flux compactification with low energy supersymmetry. Moduli are stabilized by fluxes and nonperturbative dynamics while a de Sitter vacuum is obtained by adding supersymmetry breaking anti-branes. We discuss the characteristic pattern of mass scales in such a set-up as well as some features of 4D N = 1 supergravity breakdown by anti-branes. Anomaly mediation is found to always give an important contribution and one can easily arrange for flavor-independent soft terms. In its most attractive realization, the modulus mediation is comparable to the anomaly mediation, yielding a quite distinctive sparticle spectrum. In addition, the axion component of the modulus/dilaton superfield dynamically cancels the relative CP phase between the contributions of anomaly and modulus mediation, thereby avoiding dangerous SUSY CP violation.

We investigate gaugino condensation in the framework of the strongly coupled heterotic E 8 × E 8 string (M-theory). Supersymmetry is broken in a hidden sector and gravitational interactions induce soft breaking parameters in the observable sector. The resulting soft masses are of order of the gravitino mass. The situation is similar to that in the weakly coupled E 8 × E 8 theory with one important difference: we avoid the problem of small gaugino masses which are now comparable to the gravitino mass.

We discuss radiative electroweak symmetry breaking with non-universal scalar masses at the GUT scale. Large tan β solutions are investigated in detail and it is shown that qualitatively new (as compared to the universal case) solutions exist, with much less correlation between soft terms. We identify two classes of nonuniversalities which give solutions withIn each case, after imposing gauge and Yukawa coupling unification, we discuss the predictions for m t , m b and the spectrum of supersymmetric particles. One striking consequence is the possibility of light charginos and neutralinos which in the second option can be higgsino-like. Cosmological constraint on the relic abundance of the lightest neutralino is also included.

We investigate the properties of localized anomalous U(1)'s in heterotic string theory on the orbifold T 6 /Z 3 . We argue that the local four dimensional and original ten dimensional Green-Schwarz mechanisms can be implemented simultaneously, making the theory manifestly gauge invariant everywhere, in the bulk and at the fixed points. We compute the shape of the Fayet-Iliopoulos tadpoles, and cross check this derivation for the four dimensional auxiliary fields by a direct calculation of the tadpoles of the internal gauge fields. Finally we study some resulting consequences for spontaneous symmetry breaking, and derive the profile of the internal gauge field background over the orbifold.

The infrared quasi fixed point solution for the top quark mass in the Minimal Supersymmetric Standard Model explains in a natural way large values of the top quark mass and appears as a prediction in many interesting theoretical schemes. Moreover, as has been recently pointed out, for moderate values of tan β, in order to achieve gauge and bottom-tau Yukawa coupling unification, the top quark mass must be within 10% of its fixed point value. In this work we show that the convergence of the top quark mass to its fixed point value has relevant consequences for the (assumed) universal soft supersymmetry breaking parameters at the grand unification scale. In particular, we show that the low energy parameters do not depend on A 0 and B 0 but on the combination δ = B 0 − A 0 /2. Hence, there is a reduction in the number of independent parameters. Most interesting, the radiative SU (2) L × U (1) Y breaking condition implies strong correlations between the supersymmetric mass parameter µ and the supersymmetry breaking parameters δ and M 1/2 or m 0 . These correlations, which become stronger for tan β < 2, may have some fundamental origin, which would imply the need of a reformulation of the naive fine tuning criteria.

We amplify previous discussions of the fine-tuning price to be paid by supersymmetric models in the light of LEP data, especially the lower bound on the Higgs boson mass, studying in particular its power of discrimination between different parameter regions and different theoretical assumptions. The analysis is performed using the full one-loop effective potential. The whole range of tan β is discussed, including large values. In the minimal supergravity model with universal gaugino and scalar masses, a small fine-tuning price is possible only for intermediate values of tan β. However, the fine-tuning price in this region is significantly higher if we require b − τ Yukawa-coupling unification. On the other hand, price reductions are obtained if some theoretical relation between MSSM parameters is assumed, in particular between µ 0 , M 1/2 and A 0 . Significant price reductions are obtained for large tan β if non-universal soft Higgs mass parameters are allowed. Nevertheless, in all these cases, the requirement of small fine tuning remains an important constraint on the superpartner spectrum. We also study input relations between MSSM parameters suggested in some interpretations of string theory: the price may depend significantly on these inputs, potentially providing guidance for building string models. However, in the available models the fine-tuning price may not be reduced significantly.