Related papers: The Geometry of Generations
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
We propose a texture of three generation Majorana-type neutrino mass matrix in terms of only two parameters which gives rise to nearly bi-maximal mixing angles. We also demonstrate an explicit realization of such type of neutrino…
The $tt^*$ equations define a flat connection on the moduli spaces of $2d, \mathcal{N}=2$ quantum field theories. For conformal theories with $c=3d$, which can be realized as nonlinear sigma models into Calabi-Yau d-folds, this flat…
We construct a class of Heterotic String vacua described by Landau--Ginzburg theories and consider orbifolds of these models with respect to abelian symmetries. For LG--vacua described by potentials in which at most three scaling fields are…
We describe the topology of the moduli spaces of flat metrics for all the 3-dimensional closed manifolds. We give an algebraic description of the moduli spaces for the 4-dimensional closed flat manifolds with a single generator in their…
We consider a class of special Lagrangian subspaces of Calabi-Yau manifolds and identify their mirrors, using the recent derivation of mirror symmetry, as certain holomorphic varieties of the mirror geometry. This transforms the counting of…
We consider the variant of Mirror Symmetry Conjecture for K3 surfaces which relates "geometry" of curves of a general member of a family of K3 with "algebraic functions" on the moduli of the mirror family. Lorentzian Kac--Moody algebras are…
We say a mirror pair of Calabi-Yau varieties exhibits strong arithmetic mirror symmetry if the number of points on each variety over a finite field is equivalent, modulo the order of that field. We search for strong mirror symmetry in…
Motivated by the physical concept of special geometry two mathematical constructions are studied, which relate real hypersurfaces to tube domains and complex Lagrangean cones respectively. Me\-thods are developed for the classification of…
Possible generation structure is investigated. We considere alternative possibility of combination of leptons and quarks to compose each generation, where the combination of $(\nu_{\tau},{\tau})$ and $(u,d)$ compose a generation. Our model…
We suggest a mechanism explaining the origin of three generations of the Standard Model fermions from one generation in a higher-dimensional theory. Four-dimensional fermions appear as zero modes trapped in the core of a topological defect…
Possible physical consequences of a recently discovered nonabelian dual symmetry are explored in the standard model. It is found that both Higgs fields and fermion generations can be assigned a natural place in the dual framework, with…
Schemes based on anticommuting scalar coordinates, corresponding to properties, lead to generations of particles very naturally. In contrast to the standard model, where masses arise through independent Yukawa couplings to a single Higgs…
The special geometries of two recently discovered Calabi-Yau threefolds with $h^{11}=1$ are analyzed in detail. These correspond to the 'minimal three-generation' manifolds with $h^{21}=4$ and the `24-cell' threefolds with $h^{21}=1$. It…
Recently, a new way of deriving the moduli space of quiver gauge theories that arise on the world-volume of D3-branes probing singular toric Calabi-Yau cones was conjectured. According to the proposal, the gauge group, matter content and…
We present the most complete list of mirror pairs of Calabi-Yau complete intersections in toric ambient varieties and develop the methods to solve the topological string and to calculate higher genus amplitudes on these compact Calabi-Yau…
We apply deep-learning techniques to the string landscape, in particular, $SO(32)$ heterotic string theory on simply-connected Calabi-Yau threefolds with line bundles. It turns out that three-generation models cluster in particular islands…
The Higgs sector of the Standard Model with one right-handed neutrino per family is systematically analyzed. In a model with intergenerational independent mixings between families, we can account for very light neutrinos acquiring Majorana…
Cluster varieties are geometric objects that have recently found applications in several areas of mathematics and mathematical physics. This thesis studies the geometry of a large class of cluster varieties associated to compact oriented…
We study three generation models in the four-dimensional spacetime, which can be derived from the ten-dimensional N=1 super Yang-Mills theory on the orbifold background with a non-vanishing magnetic flux. We classify the flavor structures…