Hidden Sector Supergravity Breakdown

Gravity mediated supersymmetry breakdown originated from a study of gaugino condensation in a hidden sector. We review this mechanism of supergravity breakdown from the original formulation in the early eighties to its natural implementation in superstring theory and M-theory. In the latter case hidden and observable sector become separated geometrically and supersymmetry is broken dynamically on a hidden wall.Comment: 14 pages, Latex, Invited talk presented at the symposium "Thirty Years of Supersymmetry", University of Minnesota, October 13-15, 200

Supersymmetry Breakdown at a Hidden Wall

We consider hidden sector supersymmetry breakdown in the strongly coupled heterotic $E_8\times E_8$ theory of Ho\v{r}ava and Witten. Using effective field theory methods in four dimensions, we can show that gravitational interactions induce soft breaking terms in the observable sector that are of order of the gravitiono mass. We apply these methods to the mechanism of gaugino condensation at the hidden wall. Although the situation is very similar to the weakly coupled case, there is a decisive difference concerning the observable sector gaugino mass; with desirable phenomenological as well as cosmological consequences.Comment: 29 pages, latex, no figures, To appear in Nuclear Physics B. Minor change

Stringy Origin of Discrete R-symmetries

Discrete symmetries play a crucial role in particle physics. They appear abundantly in string model constructions. We focus here on the case of discrete $R$-symmetries which are intrinsically connected to the Lorentz group in extra dimensions and the appearance of $N$-extended supersymmetry. In that sense, discrete $R$-symmetries can be understood as "fractionally" extended supersymmetry. These symmetries reveal insight about the location of fields in extra dimensions (in particular the Higgs boson). Applications can be found in the solution of the $\mu$-problem, suppression of proton decay and the structure of the soft terms of broken supersymmetry.Comment: Proceedings of the Corfu Summer Institute 2016 "School and Workshops on Elementary Particle Physics and Gravity",31 August - 23 September, 2016, Corfu, Greec

Five golden rules for superstring phenomenology

Recent measurements of the values of gauge coupling constants as well as neutrino properties support the idea of a grand unified (GUT) description of particle physics at a large scale of $M_{GUT}\sim 10^{16}$ GeV. We discuss a strategy to incorporate this picture in the framework of superstring theory. In such a scheme successful predictions of GUTs can be realized while some of the more problematic aspects of grand unification might be avoided. The most promising models are expected in the framework of the heterotic $E_8\times E_8$ string theory.Comment: Based on talks given at the conference on ``String Phenomenology 2004, Ann Arbor, and ``Pascos04-NathFest Symposium'', Boston, August 200