Dualization of non-Abelian BF model

We show that dualization of BF models to Stueckelberg-like massive gauge theories allows a non-Abelian extension. We obtain local Lagrangians which are straightforward extensions of the Abelian results.Comment: 6 pages, ReVTeX, no figures, to be publ. on Phys.Lett.

Holomorphic Bundles and the Moduli Space of N=1 Supersymmetric Heterotic Compactifications

We describe the first order moduli space of heterotic string theory compactifications which preserve $N=1$ supersymmetry in four dimensions, that is, the infinitesimal parameter space of the Strominger system. We establish that if we promote a connection on $TX$ to a field, the moduli space corresponds to deformations of a holomorphic structure $\bar D$ on a bundle $\cal Q$. The bundle $\cal Q$ is constructed as an extension by the cotangent bundle $T^*X$ of the bundle $E= {\rm End}(V) \oplus {\rm End}(TX) \oplus TX$ with an extension class $\cal H$ which precisely enforces the anomaly cancelation condition. The deformations corresponding to the bundle $E$ are simultaneous deformations of the holomorphic structures on the poly-stable bundles $V$ and $TX$ together with those of the complex structure of $X$. We discuss the fact that the "moduli" corresponding to ${\rm End}(TX)$ cannot be physical, but are however needed in our mathematical structure to be able to enforce the anomaly cancelation condition. In the Appendix we comment on the choice of connection on $TX$ which has caused some confusion in the community before. It has been shown by Ivanov and others that this connection should also satisfy the instanton equations, and we give another proof of this fact.Comment: Added references; extended section 3 to explain better the moduli space; corrected various minor errors and typos. 62 page

A Change of Variables to the Dual and Factorization of Composite Anomalous Jacobians

Changes of variables giving the dual model are constructed explicitly for sigma-models without isotropy. In particular, the jacobian is calculated to give the known results. The global aspects of the abelian case as well as some of those of the cases where the isometry group is simply connected are considered. Considering the anomalous case, we infer by a consistency argument that the `multiplicative anomaly' should be replaceable by adequate rules for factorization of composite jacobians. These rules are then generalized in a simple way for composite jacobians defined in spaces of different types. Implimentation of these rules then gives specific formulas for the anomally for semisimple algebras and also for solvable ones.Comment: 15 pages, no figures, Latex file, A treatment of the global aspects of the abelian and of semisimple duality groups are added. General formulas for the mixed anomaly are derive

EVALUATION OF THE DELTA STATE SKILLS TRAINING AND ENTREPRENEURSHIP PROGRAMME (STEP)

This study evaluated the extent to which the goals of the Delta State Skills Training and Entrepreneurship Programme (STEP) have been achieved. Three research questions guided the study. The population of the study comprised 4,559 beneficiaries. A sample size of 1,000 beneficiaries was selected through proportionate stratified and convenience sampling techniques. A questionnaire was used to collect data. Experts’ judgement was used to validate the instrument. The test-retest method of reliability was used to determine the reliability of the instrument, with a coefficient of 0.82. Frequency and percentage were used to analyse the data. The findings of the study revealed that STEP has trained beneficiaries in the following skill options: Fashion design, Catering, Hairdressing, Make-up, Fishery, Decoration and event management, Electrical installation and repairs, Welding and fabrication, ICT and Farming; all the 1000 participants evaluated have established their own enterprises, indicating a 100% goal achievement; and that majority of the beneficiaries have employed other youths after graduating from the programme. The study recommended amongst others that the program be expanded to accommodate more economically viable skills and vocations, including commerce/trade apprenticeship.  Article visualizations

Moderate levels of oxygenation during the late stage of Earth's Great Oxidation Event

The later stages of Earth's transition to a permanently oxygenated atmosphere during the Great Oxidation Event (GOE; ∼2.43–2.06 Ga) is commonly linked with the suggestion of an “oxygen overshoot” during the ∼2.22–2.06 Ga Lomagundi Event (LE), which represents Earth's most pronounced and longest-lived positive carbon isotope excursion. However, the magnitude and extent of atmosphere-ocean oxygenation and implications for the biosphere during this critical period in Earth's history remain poorly constrained. Here, we present nitrogen (N), selenium (Se), and carbon (C) isotope data, as well as bio-essential element concentrations, for Paleoproterozoic marine shales deposited during the LE. The data provide evidence for a highly productive and well-oxygenated photic zone, with both inner and outer-shelf marine environments characterized by nitrate- and Se oxyanion-replete conditions. However, the redoxcline subsequently encroached back onto the inner shelf during global-scale deoxygenation of the atmosphere-ocean system at the end of the LE, leading to locally enhanced water column denitrification and quantitative reduction of selenium oxyanions. We propose that nitrate-replete conditions associated with fully oxygenated continental shelf settings were a common feature during the LE, but nitrification was not sufficiently widespread for the aerobic nitrogen cycle to impact the isotopic composition of the global ocean N inventory. Placed in the context of Earth's broader oxygenation history, our findings indicate that O levels in the atmosphere-ocean system were likely much lower than modern concentrations. Early Paleoproterozoic biogeochemical cycles were thus far less advanced than after Neoproterozoic oxygenation.FOO and RS acknowledge financial support from the University of Tübingen and the German Research Foundation (DFG Grant SCHO1071/11-1 ). FOO and MBA are thankful for support from the Natural Environment Research Council (NERC grant NE/V004824/1 ). The stable isotope facilities at IDYST were funded by the University of Lausanne . SK, YA and MIV-R acknowledge European Research Council (ERC) Starting Grant 636808 (O2RIGIN). AH and FOO acknowledge support from National Research Foundation of South Africa (NRF Grant 75892 ). SK also acknowledges the Ramon y Cajal contract (RYC2020-030014-I). Participation by AB was supported by Discovery and Accelerator Grants from the Natural Sciences and Engineering Research Council of Canada (NSERC) and ACS PF grant ( 624840ND2 ). EES acknowledges funding from a NERC Frontiers grant ( NE/V010824/1 ). SWP acknowledges support from a Royal Society Wolfson Research Merit Award . MIV-R additionally acknowledges funding support from the German Research Foundation (DFG Grant VA 1568/1-1 )

Moderate levels of oxygenation during the late stage of Earth's Great Oxidation Event

FOO and RS acknowledge financial support from the University of Tübingen and the German Research Foundation (DFG Grant SCHO1071/11-1). FOO and MBA are thankful for support from the Natural Environment Research Council (NERC grant NE/V004824/1). The stable isotope facilities at IDYST were funded by the University of Lausanne. SK, YA and MIV-R acknowledge European Research Council (ERC) Starting Grant 636808 (O2RIGIN). AH and FOO acknowledge support from National Research Foundation of South Africa (NRF Grant 75892). SK also acknowledges the Ramon y Cajal contract (RYC2020-030014-I). Participation by AB was supported by Discovery and Accelerator Grants from the Natural Sciences and Engineering Research Council of Canada (NSERC) and ACS PF grant (624840ND2). EES acknowledges funding from a NERC Frontiers grant (NE/V010824/1). SWP acknowledges support from a Royal Society Wolfson Research Merit Award. MIV-R additionally acknowledges funding support from the German Research Foundation (DFG Grant VA 1568/1-1).The later stages of Earth's transition to a permanently oxygenated atmosphere during the Great Oxidation Event (GOE; ∼2.43–2.06 Ga) is commonly linked with the suggestion of an “oxygen overshoot” during the ∼2.22–2.06 Ga Lomagundi Event (LE), which represents Earth's most pronounced and longest-lived positive carbon isotope excursion. However, the magnitude and extent of atmosphere-ocean oxygenation and implications for the biosphere during this critical period in Earth's history remain poorly constrained. Here, we present nitrogen (N), selenium (Se), and carbon (C) isotope data, as well as bio-essential element concentrations, for Paleoproterozoic marine shales deposited during the LE. The data provide evidence for a highly productive and well-oxygenated photic zone, with both inner and outer-shelf marine environments characterized by nitrate- and Se oxyanion-replete conditions. However, the redoxcline subsequently encroached back onto the inner shelf during global-scale deoxygenation of the atmosphere-ocean system at the end of the LE, leading to locally enhanced water column denitrification and quantitative reduction of selenium oxyanions. We propose that nitrate-replete conditions associated with fully oxygenated continental shelf settings were a common feature during the LE, but nitrification was not sufficiently widespread for the aerobic nitrogen cycle to impact the isotopic composition of the global ocean N inventory. Placed in the context of Earth's broader oxygenation history, our findings indicate that O2 levels in the atmosphere-ocean system were likely much lower than modern concentrations. Early Paleoproterozoic biogeochemical cycles were thus far less advanced than after Neoproterozoic oxygenation.Publisher PDFPeer reviewe

Remarks on Non-Abelian Duality

A class of two-dimensional globally scale-invariant, but not conformally invariant, theories is obtained. These systems are identified in the process of discussing global and local scaling properties of models related by duality transformations, based on non-semisimple isometry groups. The construction of the dual partner of a given model is followed through; non-local as well as local versions of the former are discussed.Comment: 33 pages, CERN-TH.7414/94, RI-9-94, WIS-7-9