Neutrinos: Windows to Planck Physics

After recalling some elegant contributions of the late Freydoon Mansouri, we turn to neutrino physics and use a {\it modicum} of grand unification to relate quark and lepton mixing matrices. We advocate an expansion for the MNS matrix, {\it \`a la} Wolfenstein, and argue that in a wide class of models, $\theta_{13}$ is a Cabibbo mixing effect. Also the large neutrino mixing angles reflect the mass patterns of the right-handed neutrinos near the Planck scale, and provide evidence for family structure at that scale.Comment: COntribution to Quantum Theory and Symmetries COnference, Univ of Cincinatti, October 2003; Latex, 11 page

Mass Hierarchies from Anomalies: a Peek Behind the Planck Curtain

The masses of quarks and leptons suggest a strong hierarchical structure. We argue that their patterns can be reproduced through the introduction of a new Abelian symmetry. The data suggest that this symmetry is anomalous. We suggest that the cancellation of its anomalies occur through the Green-Schwarz mechanism. An important check of this idea is that it links the Weinberg angle to a mass ratio of the elementary fermions. The Green-Schwarz mechanism occurs naturally in many superstring compactifications, and produces a small parameter, which we use to determine the quark mass hierarchy. We show that hierarchy and mixings among the chiral fermions is a consequence of the Green-Schwarz mechanism. We present several models where this idea is realized.Comment: Based on a talk delivered in the honor of Professor K. Kikkawa's 60th birthday, December 1995, Osaka, Japan. Latex, 15 pages, macros include

From Neutrino Masses to Proton Decay

Current theoretical and experimental issues are reviewed in the light of the recent SuperKamiokande discovery. By using quark-lepton symmetries, derived from Grand Unification and/or string theories, we show how to determine the necessary neutrino parameters. In addition, the seesaw neutrino masses set the scale for the proton decay operators by ``measuring'' the standard model cut-off. The SuperKamiokande values suggest that proton decay is likely to be observed early in the XXIst Century.Comment: Invited Talk at the Workshop on the Next generation Nucleon decay and Neutrino detector (NNN99), September 23-25, 1999. Latex, 9 page

The Sirens of Eleven Dimensions

While most theorists are tied to the mast of four dimensions, some have found it irresistible to speculate about eleven dimensions, the domain of M-theory. We outline a program which starts from the light-cone description of supergravity, and tracks its divergences to suggest the existence of an infinite component theory which in the light-cone relies on the coset $F_4/SO(9)$, long known to be linked to the Exceptional Jordan Algebra.Comment: Contribution to "From Fields to Strings: Circumnavigating Theoretical Physics", Edited by M. Shifman, A. Vainshtein, and J. Wheater, in memory of Ian Koga