Related papers: Geometrically Engineering the Standard Model: Loca…
This study introduces a new unified structural framework for orbifold sigma models that incorporates twisted sectors, singularities, and smooth regions into a single algebraic object. Traditional approaches to orbifold theories often treat…
We construct a comprehensive list of non-supersymmetric standard model extensions with a low-scale LR-symmetric intermediate stage that may be obtained as simple low-energy effective theories within a class of renormalizable $SO(10)$ GUTs.…
Multiple scales coexist in complex networks. However, the small world property makes them strongly entangled. This turns the elucidation of length scales and symmetries a defiant challenge. Here, we define a geometric renormalization group…
I review the holographic techniques used to efficiently study models with Gauge-Higgs Unification (GHU) in one extra dimension. The general features of GHU models in flat extra dimensions are then reviewed, emphasizing the aspects related…
We analyze the gauge unification in minimal supersymmetric SO(10) grand unified theories in 5 dimensions. The single extra spatial dimension is compactified on the orbifold S^1/(Z_2 x Z_2') reducing the gauge group to that of Pati-Salam…
In family unification models, all three families of quarks and leptons are grouped together into an irreducible representation of a simple gauge group, thus unifying the Standard Model gauge symmetries and a gauged family symmetry. Large…
A review of orbifold geometry is given, followed by a review of the construction of four-dimensional heterotic string models by compactification on a six-dimensional Z_3 orbifold. Particular attention is given to the details of the…
We consider the possibility of grand unification of the $\mathrm{ SU(3)_c \otimes SU(3)_L \otimes U(1)_X}$ model in an SU(6) gauge unification group. Two possibilities arise. Unlike other conventional grand unified theories, in SU(6) one…
If a family symmetry exists for the quarks and leptons, the Higgs sector is expected to be enlarged to be able to support the transformation properties of this symmetry. There are however three possible generic ways (at tree level) of…
We study geometric engineering of four-dimensional N=1 gauge models from M-theory on a seven-dimensional manifold with G_2 holonomy. The manifold is constructed as a K3 fibration over a three-dimensional base space with ADE geometry. The…
This paper proposes a novel paradigm for machine learning that moves beyond traditional parameter optimization. Unlike conventional approaches that search for optimal parameters within a fixed geometric space, our core idea is to treat the…
In this paper we construct supersymmetric flipped SU(5) GUTs from E_8 singularities in F-theory. We start from an SO(10) singularity unfolded from an E_8 singularity by using an SU(4) spectral cover. To obtain realistic models, we consider…
A general model for geometric structures on differentiable manifolds is obtained by deforming infinitesimal symmetries. Specifically, this model consists of a Lie algebroid, equipped with an affine connection compatible with the Lie…
In comparing the behavior of an energy spectrum to the predictions of random matrix theory one must transform the spectrum such that the averaged level spacing is constant, a procedure known as unfolding. Once energy spectrums belong to an…
Symmetries play an essential role in the construction and phenomenology of quantum field theories (QFTs). We discuss how to construct symmetries of QFTs by extending minimal "seed" symmetry groups to larger groups that contain the seed(s)…
A systematic study of "lifted" Gepner models is presented. Lifted Gepner models are obtained from standard Gepner models by replacing one of the N=2 building blocks and the $E_8$ factor by a modular isomorphic $N=0$ model on the bosonic…
Maximally supersymmetric SO(10) and SU(6) unified theories are constructed on the orbifold T^2/(Z_2 x Z'_2), with one length scale R_5 taken much larger than the other, R_6. The effective theory below 1/R_6 is found to be the highly…
We study geometric properties of certain obstructed equisingular families of projective hypersurfaces with emphasis on smoothness, reducibility, being reduced, and having expected dimension. In the case of minimal obstructness, we give a…
We propose low energy 6-dimensional N=2 supersymmetric SU(6) models on $M^4\times T^2/(Z_2)^3$ and $M^4\times T^2/(Z_2)^4$, where the orbifold $SU(3)_C\times SU(3)$ model can be embedded on the boundary 4-brane. For the zero modes, the…
We construct two more supersymmetric E6 grand unified models with three generations within the framework of Z12 asymmetric orbifold compactification of the heterotic string theory. Such an asymmetric orbifold is missing in the…