Noncommutative tori and the Riemann-Hilbert correspondence

We study the interplay between noncommutative tori and noncommutative elliptic curves through a category of equivariant differential modules on $\mathbb{C}^*$. We functorially relate this category to the category of holomorphic vector bundles on noncommutative tori as introduced by Polishchuk and Schwarz and study the induced map between the corresponding K-theories. In addition, there is a forgetful functor to the category of noncommutative elliptic curves of Soibelman and Vologodsky, as well as a forgetful functor to the category of vector bundles on $\mathbb{C}^*$ with regular singular connections. The category that we consider has the nice property of being a Tannakian category, hence it is equivalent to the category of representations of an affine group scheme. Via an equivariant version of the Riemann-Hilbert correspondence we determine this group scheme to be (the algebraic hull of) $\mathbb{Z}^2$. We also obtain a full subcategory of the category of holomorphic bundles of the noncommutative torus, which is equivalent to the category of representations of $\mathbb{Z}$. This group is the proposed topological fundamental group of the noncommutative torus (understood as a degenerate elliptic curve) and we study Nori's notion of \'etale fundamental group in this context.Comment: 22 pages with major revisions. Some preliminary material removed. Section 4 on the \'etale fundamental group of noncommutative tori is entirely new. References changed accordingly, to appear in JNC

On Stability of the Three 3-brane Model

We show that the Goldberger-Wise mechanism for the three 3-brane scenario proposed by Kogan et al. stabilizes the radion. We find that the system of 3-branes stabilizes in such a way that the loss in the scale factor is insignificant. That is, the negative tension brane chooses to stay close to the visible brane

Radion effects on unitarity in gauge-boson scattering

The scalar field associated with fluctuations in the positions of the two branes, the ``radion'', plays an important role determining the cosmology and collider phenomenology of the Randall-Sundrum solution to the hierarchy problem. It is now well known that the radion mass is of order the weak scale, and that its couplings to standard model fields are order 1/TeV to the trace of the energy momentum tensor. We calculate longitudinal vector boson scattering amplitudes to explore the constraints on the radion mass and its coupling from perturbative unitarity. The scattering cross section can indeed become non-perturbative at energies prior to reaching the TeV brane cutoff scale, but only when some curvature-Higgs mixing on the TeV brane is present. We show that the coefficient of the curvature-Higgs mixing operator must be less than about 3 for the 4-d effective theory to respect perturbative unitarity up to the TeV brane cutoff scale. Mass bounds on the Higgs boson and the radion are also discussed.Comment: 17 pages, LaTeX, 5 eps figures, uses epsf.sty and axodraw.st

CHARACTERISATION OF PYROLYSIS OIL DERIVED FROM TEAK TREE SAW DUST AND RICE HUSK

The teak tree saw dust (TTSD) and rice husk (RH) were pyrolysed in a fixed bed reactor at the temperature of 450°C. The feedstock particle sizes for both the biomasses were in the range of 0.5-1.0 mm. About 33.3 and 35 wt% liquid yields were found from TTSD and RH respectively. The calorific values were recorded as 23.41 and 20.01 MJ/kg for TTSD and RH bio-oils respectively, which are slightly higher than their respective biomasses. The kinematic viscosities of the bio-oils were found to be in the range of 6.8-8.1 cSt, which are quite lower than many other bio-oils. The pH value of TTSD bio-oil (i.e., 3.4) was slightly higher than the RH bio-oil (i.e., 2.8). The bio-oils indicated acidic nature with low pH value, e.g., 2.8-3.4. The bio-oils contained mostly the carboxyl and hydroxyl functional groups to represent phenols and alcohols. Both TTSD and RH have the potential to produce pyrolysis oil; however, it requires certain upgradations to make it useful for engines

Radion effects on the production of an intermediate-mass scalar and Z at LEP II

We have studied the $e^+ e^- \to Z \phi_i \to Z jj$ process, where $\phi_i$ is the Higgs and/or radion bosons. The implications of the radion effects on the preliminary ALEPH data are also discussed. The case of the lighter radion than Higgs boson is disfavored by the ALEPH analyses of the $b$ tagged four-jet data, since the radion predominantly decays into two gluon jets due to the QCD trace anomaly. If the radion is highly degenerate in mass with the Higgs, the cross section can be increased more than at one sigma level, with natural scale of the vacuum expectation value of the radion.Comment: 10 pages, 1 Postscript figure, final version to appear in PR