Neutrino masses have been extensively studied in the context of discrete symmetries. A family permutation symmetry easily explains all neutrino oscillations and their mixing angles. However it is not obvious the embedding of such symmetry in a grand unified theory where all fermions live in the same representation. We show that it is possible to embed such a horizontal discrete symmetry in a gr...

In previous work, we found that necessary and sufficient conditions for large Nc equivalence between parent and daughter theories, for a wide class of orbifold projections of U(Nc) gauge theories, are just the natural requirements that the discrete symmetry used to define the projection not be spontaneously broken in the parent theory, and the discrete symmetry permuting equivalent gauge group ...

Abstract Coherent vortex structures are fascinating physical objects that widespread in nature: from large scale atmospheric phenomena, such as tornadoes and the Great Red Spot of Jupiter to microscopic size topological defects quantum physics optics. Unlike classical dynamics fluids, optical vortices feature new interesting properties. For instance, novel discrete can be generated photonic lat...

The so-called Takahashi's \emph{Inversion Theorem}, the reconstruction of a given spinor based on its bilinear covariants, are re-examined, considering alternative dual structures. In contrast to classical results, where Dirac structure plays central role, new duals built using discrete symmetries $\mathcal{C}, \mathcal{P}, \mathcal{T}$. Their combinations also taken into account. Furthermore, ...