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

Anomalous U(1) gauge symmetries and heterotic-typeI/II string duality

Anomalous U(1) gauge symmetries can appear both in heterotic and type I string theories. In the heterotic case we find a single anomalous U(1), while in open string theories several such symmetries can appear. Nonetheless, there is a conjectured duality symmetry that might connect these two theories. We review the properties of anomalous gauge symmetries in various string theories as well as the status of this heterotic-type I/II duality. We also comment on the possible phenomenological applications of anomalous gauge symmetries in string theory.Comment: 7 pages, Latex, JHEP, Contribution to the Proceedings of TMR99, European Program Meeting on Quantum Aspects of Gauge Theories, Supersymmetry and Unification, Paris, September 199