Related papers: The Transition Function of $G_2$ over $S^6$
In the paper the notion of truncating twisting function $\tau :X\to Q$ from a simplicial set $X$ to a cubical set $Q$ and the corresponding notion of twisted Cartesian product of these sets $X\times_{\tau}Q$ are introduced. The latter…
This paper is on the connecting homomorphism in the long exact homotopy sequence of the evaluation fibration $ev_{p_0}:C(P,K)^K \to K$, where $C(P,K)^K \cong Gau(P)$ is the gauge group of a continuous principal $K$-bundle $P$ over a closed…
The semi-simple unification model based on SU(5)_GUT \times U(3)_H gauge group is an interesting extension of the minimal SU(5)_GUT grand unification theory (GUT), since it solves the two serious problems in the standard GUT: the…
Based on the generalized gauge theory on $M^4\times Z_2\times Z_3$, we reconstructed the realistic SU(5) Grand Unified model by a suitable assignment of fermion fields. The action of group elements $Z_2$ on fermion fields is the charge…
Let $U$ be a regular connected affine semi-local scheme over a field $k$. Let $G$ be a reductive group scheme over $U$. Assuming that $G$ has an appropriate parabolic subgroup scheme, we prove the following statement. Given an affine…
We consider a 6-dimensional supersymmetric SU(6) gauge theory and compactify two extra-dimensions on a multiply-connected manifold with non-trivial topology. The SU(6) is broken down to the Standard Model gauge groups in two steps by an…
A symbolic calculus for a pseudo-differential operators acting on sections of a homogeneous vector bundle over a compact homogeneous space $G/H$ with compact $G$ and $H$ is developed. We realize the symbol of a pseudo-differential operator…
We construct sphere fibrations over $(n-1)$-connected $2n$-manifolds such that the total space is a connected sum of sphere products. More precisely, for $n$ even, we construct fibrations $S^{n-1} \to \#^{k-1}(S^n \times S^{2n-1}) \to M_k$,…
We show that the spin connection of the standard metric on a six-dimensional sphere gives an exact solution to the generalized self-dual equations suggested by Tchrakian some years ago. We work on an SO(6) gauge theory with a…
In this paper we show that any $\mathbb{A}^2$-fibration over a discrete valuation ring which is also an $\mathbb{A}^2$-form is necessarily a polynomial ring. Further we show that separable $\mathbb{A}^2$-forms over PIDs are trivial.
We use F-theory to study gauge algebra preserving transitions of 6d supergravity theories that are connected by superconformal points. While the vector multiplets remain unchanged, the hyper- and tensor multiplet sectors are modified. In 6d…
There is a beautiful correspondence between configurations of lines on a rational surface and tautological bundles over that surface. We extend this correspondence to families, by means of a generalized Fourier-Mukai transform that relates…
We consider the notion of a connection on a principal bundle $P(M,G)$ from the point of view of the action of the tangential group $TG$. This leads to a new definition of a connection and allows to interpret gauge transformations as effect…
Let $G'$ be a closed subgroup of a topological group $G$. A principal $G$-bundle $X$ is reducible to a locally trivial principal $G'$-bundle $X'$ if and only if there exists a local trivialisation of $X$ such that all transition functions…
We derive the exact semiclassical expression for the second inertial parameter $\cal B$ for the superfluid and normal phases. Interpolation between these limiting values shows that the function ${\cal B}(I)$ changes sign at the spin $I_c$,…
We present the formulae for twist quantization of $g_2$, corresponding to the solution of classical YB equation with support in the 8-dimensional Borel subalgebra of $g_2$. The considered chain of twists consists of the four factors…
If P, B, H are the algebras of the total space, the base space, and the structure group of a locally trivial principal fibre bundle (QPFB), left (right) gauge transformations are defined as automorphisms of the left (right) B-module P which…
We investigate the commutativity of global products of functions on the two-sphere from the point of view of a construction started in [RT] and named the skewed product. We complete the construction of the skewed product of functions on the…
The transition form factor of $\pi^0\gamma^*\gamma^* is found. The slope is predicted. The contribution to muon g-2 is calculated.
An isotrivially fibred surface is a smooth projective surface endowed with a morphism onto a curve such that all the smooth fibres are isomorphic to each other. The first goal of this paper is to classify the isotrivially fibred surfaces…