Nontrivial Deformation of a Trivial Bundle

The ${\rm SU}(2)$-prolongation of the Hopf fibration $S^3\to S^2$ is a trivializable principal ${\rm SU}(2)$-bundle. We present a noncommutative deformation of this bundle to a quantum principal ${\rm SU}_q(2)$-bundle that is not trivializable. On the other hand, we show that the ${\rm SU}_q(2)$-bundle is piecewise trivializable with respect to the closed covering of $S^2$ by two hemispheres intersecting at the equator.Comment: The present paper has been extracted from an earlier version of arXiv:1101.0201, so that there are some overlaps in introductory parts and standard definition

Color octet scalars and high p_T four-jet events at the LHC

We study the effect of color octet scalars on the high transverse momenta four-jet cross section at the LHC. We consider both weak singlet and doublet scalars, concentrating on the case of small couplings to quarks. We find that a relatively early discovery at the LHC is possible for a range of scalar masses

Dark Matter from Unification of Color and Baryon Number

We analyze a recently proposed extension of the Standard Model based on the SU(4) x SU(2)_L x U(1)_X gauge group, in which baryon number is interpreted as the fourth color and dark matter emerges as a neutral partner of the ordinary quarks under SU(4). We show that under well-motivated minimal flavor-violating assumptions the particle spectrum contains a heavy dark matter candidate which is dominantly the partner of the right-handed top quark. Assuming a standard cosmology, the correct thermal relic density through freeze-out is obtained for dark matter masses around 2 - 3 TeV. We examine the constraints and future prospects for direct and indirect searches for dark matter. We also briefly discuss the LHC phenomenology, which is rich in top quark signatures, and investigate the prospects for discovery at a 100 TeV hadron collider.Comment: 6 pages, 5 figure

Finite closed coverings of compact quantum spaces

We show that a projective space P^\infty(Z/2) endowed with the Alexandrov topology is a classifying space for finite closed coverings of compact quantum spaces in the sense that any such a covering is functorially equivalent to a sheaf over this projective space. In technical terms, we prove that the category of finitely supported flabby sheaves of algebras is equivalent to the category of algebras with a finite set of ideals that intersect to zero and generate a distributive lattice. In particular, the Gelfand transform allows us to view finite closed coverings of compact Hausdorff spaces as flabby sheaves of commutative C*-algebras over P^\infty(Z/2).Comment: 26 pages, the Teoplitz quantum projective space removed to another paper. This is the third version which differs from the second one by fine tuning and removal of typo