Phenomenology with Supersymmetric Flipped SU(6)

The supersymmetric flipped $SU(6)\times U(1)$ gauge symmetry can arise through compactification of the ten dimensional $E_8\times E_8$ superstring theory. We show how realistic phenomenology can emerge from this theory by supplementing it with the symmetry ${\cal R}\times {\cal U}(1)$, where ${\cal R}$ denotes a discrete `R'-symmetry. The well-known doublet-triplet splitting problem is resolved to `all orders' via the pseudo-Goldstone mechanism, and the GUT scale arises from an interplay of the Planck and supersymmetry breaking scales. The symmetry ${\cal R}\times {\cal U}(1)$ is also important for understanding the fermion mass hierarchies as well as the magnitudes of the CKM matrix elements. Furthermore, the well known MSSM parameter $\tan \beta $ is estimated to be of order unity, while the proton lifetime ($\tau_p\sim 10^2\tau_{pSU(5)}$) is consistent with observations. Depending on some parameters, $p\to K\mu^+ $ can be the dominant decay mode. Finally, the observed solar and atmospheric neutrino `anomalies' require us to introduce a `sterile' neutrino state. Remarkably, the ${\cal R}\times {\cal U}(1)$ symmetry protects it from becoming heavy, so that maximal angle $\nu_{\mu}$ oscillations into a sterile state can explain the atmospheric anomaly, while the solar neutrino puzzle is resolved via the small angle $\nu_e-\nu_{\tau}$ MSW oscillations. The existence of some ($\sim 15 - 20% $ of critical energy density) neutrino hot dark matter is also predicted.