Related papers: The Freund-Rubin Coset, Textures and Group Theory
Talk based on work entitled ``Yukawa textures, new physics and nondecoupling,'' done in collaboration with G. C. Branco and J. I. Silva-Marcos, arXiv:hep-ph/0612252, to appear in Phys. Rev. D. In this work we pointed out that New Physics…
We describe the generalized Matsuda's theorem, and some results of a Burnside ring extend a partial Burnside ring. In particular, we give isomorphism between partial Burnside rings of different groups. Moreover, we consider the relationship…
The fermion mass textures are discussed in the context of F-theory SU(5) GUT. The tree-level up, down and charged lepton Yukawa couplings are computed in terms of the integrals of overlapping wavefunctions at the intersection points of…
The Yukawa textures of effective heterotic models are studied by using singular spectral data. One advantage of this approach is that it is possible to dissect the cohomologies of the bundles into smaller parts and identify the pieces that…
We study the coupling selection rules associated with non-group symmetries, i.e., $\mathbb{Z}_2$ gauging of $\mathbb{Z}_M$ symmetries. We clarify which Yukawa textures can be derived by our selection rules for $M=3, 4$, and 5, and obtain…
In a series of papers, we have shown that from the representatio theory of a compact groupoid one can reconstruct the groupoid using the procedure similar to the Tannaka-Krein duality for compact groups. In this part we study continuous…
We show that the Freiman--Ruzsa theorem, characterising finite sets with bounded doubling, leads to an alternative proof of a characterisation of Meyer sets, that is, relatively dense subsets of Euclidean spaces whose difference sets are…
We utilise the duality between M theory and Type IIA string theory to show the existence of Freund-Rubin compactifications of M theory on 7-manifolds with singularities supporting chiral fermions. This leads to a concrete way to study…
The general structure of the matter Kahler metric in the $\kappa^{2/3}$ expansion of Horava-Witten M-theory with nonstandard embeddings is examined. It is shown that phenomenological models based on this structure can lead to Yukawa and…
This is a reference volume on polyfold and Fredholm theory.
Phenomenological aspects of non-invertible symmetries, in particular the flavor structure of quarks and leptons, are studied. We start with a $\mathbb{Z}_M$ discrete symmetry and gauge $\mathbb{Z}_2$ so as to obtain a non-invertible…
These notes are a part of my lectures on representations of adelic groups attached to two-dimensional schemes. They contain a study of the one-dimensional case as a preliminary step to the case of dimension two. We consider the following…
The text deals with generalizations of the Markoff equation in number theory, arising from continued fractions. It gives the method for the complete resolution of such new equations, and their interpretation in algebra and algebraic…
We establish a new Iwasawa theory for the kernel of Frobenius on Jacobians of curves in geometric $\mathbf{Z}_p$-towers over the projective line in characteristic $p$, thereby proving several of the main conjectures of [arXiv:2107.12555].
We point out that New Physics can play an important r\^ ole in rescuing some of the Yukawa texture zero ans\" atze which would otherwise be eliminated by the recent, more precise measurements of $V_{CKM}$. As an example, a detailed analysis…
Motivated by potential phenomenological applications, we develop the necessary tools for building GUT models in F-theory. This approach is quite flexible because the local geometrical properties of singularities in F-theory…
This article is devoted to the investigation of wrap groups of connected fiber bundles. CW-groups associated with wrap groups are studied.
This article has the following aims: (1) Extend the notion of fuchsian singularities (of first kind) to base fields of arbitrary characteristic. (2) Discuss their relationship to mathematical objects of a different nature. (3) Provide a…
Hrushovski's suggestion, given in ["Groupoids, imaginaries and internal covers," Turkish Journal of Mathematics , 2012], to capture the structure of the 1-analysable covers of a theory T using simplicial groupoids definable in T is realized…
We computed the first Whittaker coefficient of an Eisenstein series on a global metaplectic group induced from the torus and related the result with a Weyl group multiple Dirichlet series attached to the (dual) root system of the group…