Discretized gravity on the hyperbolic disk

We consider a description of lattice gravity in six dimensions, where the two extra dimensions have been compactified on a warped hyperbolic disk of constant curvature. We analyze a fine-grained latticization of the hyperbolic disk in the context of an effective theory for massive gravitons. We find that in six-dimensional warped hyperbolic space, lattice gravity appears near the boundary of the disk more weakly coupled than in discretized five-dimensional flat or warped space. Specifically, near the IR branes, the local strong coupling scale can become as large as the local Planck scale.Comment: 4 pages, 2 figures, to appear in Proceedings of SUSY06, the 14th Conference on Supersymmetry and the Unification of Fundamental Interactions, UC Irvine, California, 12-17 June 200

Neutrino Oscillations in Deconstructed Dimensions

We present a model for neutrino oscillations in the presence of a deconstructed non-gravitational large extra dimension compactified on the boundary of a two-dimensional disk. In the deconstructed phase, sub-mm lattice spacings are generated from the hierarchy of energy scales between 1 TeV and the usual B-L breaking scale 10^{15} GeV. Here, short distance cutoffs down to 1 eV can be motivated by the strong coupling behavior of gravity in local discrete extra dimensions. This could make it possible to probe the discretization of extra dimensions and non-trivial field configurations in theory spaces which have only a few sites, i.e., for coarse latticizations. Thus, the model has relevance to present and future precision neutrino oscillation experiments.Comment: 38 pages, 11 figures, typos correcte

See-saw Mechanisms for Dirac and Majorana Neutrino Masses

We investigate the see-saw mechanism for generally non-fine-tuned $n \times n$ mass matrices involving both Dirac and Majorana neutrinos. We specifically show that the number of naturally light neutrinos cannot exceed half of the dimension of the considered mass matrix. Furthermore, we determine a criterion for mass matrix textures leading to light Dirac neutrinos with the see-saw mechanism. Especially, we study $4 \times 4$ and $6 \times 6$ mass matrix textures and give some examples in order to highlight these types of textures. Next, we present a model scheme based on non-Abelian and discrete symmetries fulfilling the above mentioned criterion for light Dirac neutrinos. Finally, we investigate the connection between symmetries and the invariants of a mass matrix on a formal level.Comment: 12 pages, RevTeX. Final version to be published in Phys. Rev.