Geometric constraints in dual F-theory and heterotic string compactifications

We systematically analyze a broad class of dual heterotic and F-theory models that give four-dimensional supergravity theories, and compare the geometric constraints on the two sides of the duality. Specifically, we give a complete classification of models where the heterotic theory is compactified on a smooth Calabi-Yau threefold that is elliptically fibered with a single section and carries smooth irreducible vector bundles, and the dual F-theory model has a corresponding threefold base that has the form of a P^1 bundle. We formulate simple conditions for the geometry on the F-theory side to support an elliptically fibered Calabi-Yau fourfold. We match these conditions with conditions for the existence of stable vector bundles on the heterotic side, and show that F-theory gives new insight into the conditions under which such bundles can be constructed. In particular, we find that many allowed F-theory models correspond to vector bundles on the heterotic side with exceptional structure groups, and determine a topological condition that is only satisfied for bundles of this type. We show that in many cases the F-theory geometry imposes a constraint on the extent to which the gauge group can be enhanced, corresponding to limits on the way in which the heterotic bundle can decompose. We explicitly construct all (4962) F-theory threefold bases for dual F-theory/heterotic constructions in the subset of models where the common twofold base surface is toric, and give both toric and non-toric examples of the general results.Comment: 81 pages, 2 figures; v2, v3: references added, minor corrections; v4: minor errors, Table 5 correcte

Charles W. Peach, palaeobotany and Scotland

The move south from Wick to the city of Edinburgh in 1865, some four years after retirement from the Customs service, provided Charles W. Peach with new opportunities for fossil-collecting and scientific networking. Here he renewed and maintained his interest in natural history and made significant palaeobotanical collections from the Carboniferous of the Midland Valley of Scotland. These are distinguished by some interesting characteristics of their documentation which the following generations of fossil collectors and researchers would have done well to emulate. Many of his fossil plant specimens have not only the locality detail,but also the date, month and year of collection neatly handwritten on attached paper labels; as a result, we can follow Peach's collecting activities over a period of some 18 years or so. Comments and even illustrative sketches on the labels of some fossils give us first-hand insight into Peach's observations. Study of these collections now held in National Museums Scotland reveals a pattern of collecting heavily biased towards those localities readily accessible from the newly expanding railways which provided a relatively inexpensive and convenient means of exploring the geology of the neighbourhood of Edinburgh. Charles W. Peach had a very 'hands-on' practical approach to scientific investigation which led him to construct novel glass plates with mounted Sphenopteris cuticle, removed intact from Lower Carboniferous shales and limestones originating in West Lothian. These resemble the herbarium sheets with which he was familiar from his parallel and highly significant work on extant flora including nearshore marine algae. He also prepared hand ground glass microscope slides,particularly of permineralised plant material from Pettycur in Fife, using whatever materials he had to hand at the time. Peach's collection raises questions about the evolution of accepted standards of documentation in private collections, in parallel with the evolution of collecting practices by the new professionals such as the workers of the Geological Survey. Its relatively rapid deposition in museums,compared to many private collections, may also have contributed to its apparently high rate of usage by contemporary workers

Matter in transition

We explore a novel type of transition in certain 6D and 4D quantum field theories, in which the matter content of the theory changes while the gauge group and other parts of the spectrum remain invariant. Such transitions can occur, for example, for SU(6) and SU(7) gauge groups, where matter fields in a three-index antisymmetric representation and the fundamental representation are exchanged in the transition for matter in the two-index antisymmetric representation. These matter transitions are realized by passing through superconformal theories at the transition point. We explore these transitions in dual F-theory and heterotic descriptions, where a number of novel features arise. For example, in the heterotic description the relevant 6D SU(7) theories are described by bundles on K3 surfaces where the geometry of the K3 is constrained in addition to the bundle structure. On the F-theory side, non-standard representations such as the three-index antisymmetric representation of SU(N) require Weierstrass models that cannot be realized from the standard SU(N) Tate form. We also briefly describe some other situations, with groups such as Sp(3), SO(12), and SU(3), where analogous matter transitions can occur between different representations. For SU(3), in particular, we find a matter transition between adjoint matter and matter in the symmetric representation, giving an explicit Weierstrass model for the F-theory description of the symmetric representation that complements another recent analogous construction.Comment: 107 pages, 3 figures, 32 tables. In version 2, one figure and comments added on the geometry of matter transition

Zero temperature black holes in semiclassical gravity

The semiclassical Einstein equations are solved to first order in $\epsilon = \hbar/M^2$ for the case of an extreme or nearly extreme Reissner-Nordstr\"{o}m black hole perturbed by the vacuum stress-energy of quantized free fields. It is shown that, for realistic fields of spin 0, 1/2, or 1, any zero temperature black hole solution to the equations must have an event horizon at $r_h < |Q|$, with $Q$ the charge of the black hole. It is further shown that no black hole solutions with $r_h < |Q|$ can be obtained by solving the semiclassical Einstein equations perturbatively.Comment: 7 pages, to appear in the Proceedings of the Ninth Marcel Grossmann Meeting, change in titl

Online Resources for Identifying Evidence-Based, Out-of-School Time Programs: A User's Guide

Summarizes general information, select program outcomes, and evidence levels of searchable databases, interactive summaries, and documents online on evidence-based intervention programs. Outlines considerations and assessments for selecting programs

School Improvement Plan

Students in schools display a variety of behaviors. Some of these behaviors being negative, and some of these behaviors being positive. This school improvement plan will give you a small glimpse at a Title 1 elementary school with a goal of decreasing the amount of times a student has to be removed from the classroom, or receives a first responder call. A first responder call is when an adult in the building has to call for additional adult support due to a student\u27s behaviors. This project will start with a literature review of multiple articles discussing social skills, and the the benefits of teaching social skills using the Zones of Regulation curriculum. The project will then look at the school improvement plan to see the initial data, the methodology/plan to improve the data, and the assessment tools that will be used to gather data

Developing a Low-Cost Sensor for Comparative Analysis of High Frequency Wind Speed Fluctuations

OCN 499 - Undergraduate Thesi