Related papers: Left-Right Gauge Model in Nonassociative Geometry
We study deformation quantization of nonassociative algebras whose associator satisfies some symmetric relations. This study is expanded to a larger class of nonassociative algebras includind Leibniz algebras. We apply also to this class…
In terms of non-commutative geometry, we show that the $\sigma$--model can be built up by the gauge theory on discrete group $Z_2$. We introduce a constraint in the gauge theory, which lead to the constraint imposed on linear $\sigma$ model…
A self-consistent version of the left-right (LR) symmetric model is used to examine tree- as well as one-loop level radiative corrections to the muon decay. It is shown that constraints on the heavy sector of the model parameters are…
Using a reformulation of the nonlinear multiplet as a gauge multiplet, we discuss its dynamics. We show that the nonlinear ``duality'' that appears to relate the model to a conventional $\sigma$-model introduces a new sector into the…
The main non-associative algebras are Lie algebras and Jordan algebras. There are several ways to unify these non-associative algebras and associative algebras.
In this letter we show a kind of \mt gauge symmetry can be unified into a simple group with the standard model gauge symmetry in the context of coset space unification. We also discuss some implication from one of this kind of unification.
We develop techniques for classifying the nonnegatively curved left-invariant metrics on a compact Lie group G. We prove rigidity theorems for general G and a partial classification for G=SO(4). Our approach is to reduce the general…
We generalize the background gauge in the Matrix model to propose a new gauge which is useful for discussing the conformal symmetry. In this gauge, the special conformal transformation (SCT) as the isometry of the near-horizon geometry of…
I review the recent efforts in the search for a minimal and predictive nonsupersymmetric SO(10) Grand Unified Thoery (GUT). The outcome is the revival of a minimal scenario in which a long standing result, claiming the incompatibility…
Non-associtive algebras is a research direction gaining much attention these days. New developments show that associative algebras and some not-associative structures can be unified at the level of Yang-Baxter structures. In this paper, we…
We define and investigate a geometric object, called an associative geometry, corresponding to an associative algebra (and, more generally, to an associative pair). Associative geometries combine aspects of Lie groups and of generalized…
We define and investigate a geometric object, called an associative geometry, corresponding to an associative algebra (and, more generally, to an associative pair). Associative geometries combine aspects of Lie groups and of generalized…
A structure of a left-symmetric algebra on the set of all derivations of a free algebra is introduced such that its commutator algebra becomes the usual Lie algebra of derivations. Left and right nilpotent elements of left-symmetric…
We study the origin of electroweak symmetry under the assumption that $SU(4)_{\rm C} \times SU(2)_{\rm L} \times SU(2)_{\rm R}$ is realized on a five-dimensional space-time. The Pati-Salam type gauge symmetry is reduced to $SU(3)_{\rm C}…
We systematically develop the metric aspects of nonassociative differential geometry tailored to the parabolic phase space model of constant locally non-geometric closed string vacua, and use it to construct preliminary steps towards a…
Gauge symmetries emerge from a redundant description of the effective action for light degrees of freedom after the decoupling of heavy modes. This redundant description avoids the use of explicit constraints in configuration space. For…
We review the construction of particle physics models in the framework of non-commutative geometry. We first give simple examples, and then progress to outline the Connes-Lott construction of the standard Weinberg-Salam model and our…
The problem of neutrino masses and mixing angles is analysed in a class of supersymmetric grand unified models, with SO(10) gauge symmetry and global U(2) flavour symmetry. Adopting the seesaw mechanism for the generation of the neutrino…
We suggest a new left-right symmetric grand unified model by extending Pati-Salam group to contain an isospin SU(2) and a flavor SO(3) subgroup, where the superheavy fermions are introduced as a mirror to the low-energy standard model…
We examine some recent developments in noncommutative geometry, including spin geometries on noncommutative tori and their quantization by the Shale-Stinespring procedure, as well as the emergence of Hopf algebras as a tool linking index…