On the Classification of 6D SCFTs and Generalized ADE Orbifolds

We study (1,0) and (2,0) 6D superconformal field theories (SCFTs) that can be constructed in F-theory. Quite surprisingly, all of them involve an orbifold singularity C^2 / G with G a discrete subgroup of U(2). When G is a subgroup of SU(2), all discrete subgroups are allowed, and this leads to the familiar ADE classification of (2,0) SCFTs. For more general U(2) subgroups, the allowed possibilities for G are not arbitrary and are given by certain generalizations of the A- and D-series. These theories should be viewed as the minimal 6D SCFTs. We obtain all other SCFTs by bringing in a number of E-string theories and/or decorating curves in the base by non-minimal gauge algebras. In this way we obtain a vast number of new 6D SCFTs, and we conjecture that our construction provides a full list.Comment: v3: 47 pages, 3 figures, clarifications added, typos corrected, references added, and Mathematica file update

Atomic Classification of 6D SCFTs

We use F-theory to classify possibly all six-dimensional superconformal field theories (SCFTs). This involves a two step process: We first classify all possible tensor branches allowed in F-theory (which correspond to allowed collections of contractible spheres) and then classify all possible configurations of seven-branes wrapped over them. We describe the first step in terms of "atoms" joined into "radicals" and "molecules," using an analogy from chemistry. The second step has an interpretation via quiver-type gauge theories constrained by anomaly cancellation. A very surprising outcome of our analysis is that all of these tensor branches have the structure of a linear chain of intersecting spheres with a small amount of possible decoration at the two ends. The resulting structure of these SCFTs takes the form of a generalized quiver consisting of ADE-type nodes joined by conformal matter. A collection of highly non-trivial examples involving E8 small instantons probing an ADE singularity is shown to have an F-theory realization. This yields a classification of homomorphisms from ADE subgroups of SU(2) into E8 in purely geometric terms, largely matching results obtained in the mathematics literature from an intricate group theory analysis.Comment: v3: 123 pages, 23 figures, typos corrected. Included with the submission are the Mathematica notebooks "Bases.nb" and "Fiber_Enhancements.nb

Corrosion, transport, and deposition in pressurised water nuclear reactor primary coolant systems

Several unscheduled shut downs of the Cruas nuclear power plant in France have been caused by the deposition of corrosion products in flow broaches of the steam generator tube support sheets. The depositions are theorised to be the result of electrokinetically stimulated deposition. In this work, a hot water loop to replicate these depositions in the laboratory was built, along with rigs to characterise supporting phenomena – the corrosion rate of stainless steel and the solubility of the corrosion products. While the data obtained from the hot water loop did not provide conclusive proof of the existence or prevalence of the electrokinetically stimulated deposition mechanism, evidence of deposition caused by cavitation was found. The corrosion rate of stainless steel was measured at high temperatures in solutions of lithium hydroxide at various concentrations. Surface finish was found to have an effect on the corrosion rate, though the difference between mechanically ground surfaces with an order of magnitude difference in roughness was found to be minimal. The solubility of the corrosion products formed was measured and found to be of similar order to that reported in the literature, however the minor alloying elements were found to leach from the surface in substantial quantities

6D SCFTs and phases of 5D theories

Starting from 6D superconformal field theories (SCFTs) realized via F-theory, we show how reduction on a circle leads to a uniform perspective on the phase structure of the resulting 5D theories, and their possible conformal fixed points. Using the correspon-dence between F-theory reduced on a circle and M-theory on the corresponding elliptically fibered Calabi-Yau threefold, we show that each 6D SCFT with minimal supersymmetry directly reduces to a collection of between one and four 5D SCFTs. Additionally, we find that in most cases, reduction of the tensor branch of a 6D SCFT yields a 5D generalization of a quiver gauge theory. These two reductions of the theory often correspond to different phases in the 5D theory which are in general connected by a sequence of flop transitions in the extended Kähler cone of the Calabi-Yau threefold. We also elaborate on the structure of the resulting conformal fixed points, and emergent flavor symmetries, as realized by M-theory on a canonical singularity

Structural and dielectric studies of the phase behaviour of the topological ferroelectric La1-xNdxTaO4

We thank the University of St Andrews and EPSRC (via DTG studentships to CALD and JG) for funding,The layered perovskite LaTaO4 has been prepared in its polar orthorhombic polymorphic form at ambient temperature. Although no structural phase transition is observed in the temperature interval 25° C < T < 500 °C, a very large axial thermal contraction effect is seen, which can be ascribed to an anomalous buckling of the perovskite octahedral layer. The non-polar monoclinic polymorph can be stabilised at ambient temperature by Nd-doping. A composition La0.90Nd0.10TaO4 shows a first-order monoclinic-orthorhombic (non-polar to polar) transition in the region 250° C < T < 350 °C. Dielectric responses are observed at both the above structural events but, despite the ‘topological ferroelectric’ nature of orthorhombic LaTaO4, we have not succeeded in obtaining ferroelectric P–E hysteresis behaviour. Structural relationships in the wider family of AnBnX3n+2 layered perovskites are discussed.Publisher PDFPeer reviewe

Supreme Court Brief Amicus Curiae of Administrative Law Scholars in Support of Neither Party

This brief on behalf of 29 administrative law scholars takes no position on whether Administrative Law Judges (ALJs) are employees or inferior officers. It urges the Court to issue an opinion that respects the decision that Congress made unanimously in 1946 to enact numerous statutory safeguards that assure that ALJs have decisional independence from the agencies where they work while assuring that agencies retain control over the policy content and legal basis for any decision made in an adjudication in which an ALJ presides. The brief describes the fifteen years of study and deliberation that led to the unanimous decision of Congress to enact the Administrative Procedure Act (APA) in 1946. It describes the particular attention that Congress devoted to the critical task of providing ALJs with the combination of statutory safeguards that minimize the risk that they will favor the agencies for whom they adjudicate cases while assuring that the agencies retain control of the policy content of any decision made in such an adjudication. It then describes the series of opinions the Supreme Court issued during the 1950s in which the Justices unanimously praised the provisions of the APA that assure that ALJs conduct adjudicatory hearings in an unbiased manner, explained the importance of those statutory provisions in protecting the values reflected in the Due Process Clause, and urged Congress to make those safeguards applicable to all agency adjudications. It concludes by urging the Court to issue an opinion that respects the decision that Congress made in 1946 to insulate ALJs from potential sources of pro-agency bias by including in the APA a combination of provisions that confer decisional independence on ALJs

Maximizing geographical efficiency : An analysis of the configuration of Colorado’s trauma system

ACKNOWLEDGEMENT The data used for this study were supplied by the Health Facilities and Emergency Medical Services Division of the Colorado Department of Public Health and Environment, which specifically disclaims responsibility for any analyses, interpretations, or conclusions it has not provided. The data used for this study were supplied by the Health Facilities and Emergency Medical Services Division of the Colorado Department of Public Health and Environment, which specifically disclaims responsibility for any analyses, interpretations, or conclusions it has not provided.Peer reviewedPostprin