AdS4 backgrounds with N>16 supersymmetries in 10 and 11 dimensions

We explore all warped $AdS_4\times_w M^{D-4}$ backgrounds with the most general allowed fluxes that preserve more than 16 supersymmetries in $D=10$- and $11$-dimensional supergravities. After imposing the assumption that either the internal space $M^{D-4}$ is compact without boundary or the isometry algebra of the background decomposes into that of AdS$_4$ and that of $M^{D-4}$, we find that there are no such backgrounds in IIB supergravity. Similarly in IIA supergravity, there is a unique such background with 24 supersymmetries locally isometric to $AdS_4\times \mathbb{CP}^3$, and in $D=11$ supergravity all such backgrounds are locally isometric to the maximally supersymmetric $AdS_4\times S^7$ solution.Comment: 53 pages. v2: minor changes and references added. v3: typos corrected and minor footnote added, published versio

Topological Invariants and Fibration Structure of Complete Intersection Calabi-Yau Four-Folds

We investigate the mathematical properties of the class of Calabi-Yau four-folds recently found in [arXiv:1303.1832]. This class consists of 921,497 configuration matrices which correspond to manifolds that are described as complete intersections in products of projective spaces. For each manifold in the list, we compute the full Hodge diamond as well as additional topological invariants such as Chern classes and intersection numbers. Using this data, we conclude that there are at least 36,779 topologically distinct manifolds in our list. We also study the fibration structure of these manifolds and find that 99.95 percent can be described as elliptic fibrations. In total, we find 50,114,908 elliptic fibrations, demonstrating the multitude of ways in which many manifolds are fibered. A sub-class of 26,088,498 fibrations satisfy necessary conditions for admitting sections. The complete data set can be downloaded at http://www-thphys.physics.ox.ac.uk/projects/CalabiYau/Cicy4folds/index.html .Comment: 25 pages, 7 figures, 1 table. v2: references added and minor changes. Final version accepted for publicatio

Yang-Mills solutions and Spin(7)-instantons on cylinders over coset spaces with G2G_2-structure

We study $\mathfrak{g}$-valued Yang-Mills fields on cylinders $Z(G/H)=\mathbb{R} \times G/H$, where G/H is a compact seven-dimensional coset space with $G_2$-structure, $\mathfrak{g}$ is the Lie algebra of G, and Z(G/H) inherits a Spin(7)-structure. After imposing a general G-invariance condition, Yang-Mills theory with torsion on Z(G/H) reduces to Newtonian mechanics of a point particle moving in $\mathbb{R}^n$ under the influence of some quartic potential and possibly additional constraints. The kinematics and dynamics depends on the chosen coset space. We consider in detail three coset spaces with nearly parallel $G_2$-structure and four coset spaces with SU(3)-structure. For each case, we analyze the critical points of the potential and present a range of finite-energy solutions. We also study a higher-dimensional analog of the instanton equation. Its solutions yield G-invariant Spin(7)-instanton configurations on Z(G/H), which are special cases of Yang-Mills configurations with torsion.Comment: 1+52 pages, 3 figures, 4 tables. v2: minor changes to match published versio

Chern-Simons flows on Aloff-Wallach spaces and Spin(7)-instantons

Due to their explicit construction, Aloff-Wallach spaces are prominent in flux compactifications. They carry G_2-structures and admit the G_2-instanton equations, which are natural BPS equations for Yang-Mills instantons on seven-manifolds and extremize a Chern-Simons-type functional. We consider the Chern-Simons flow between different G_2-instantons on Aloff-Wallach spaces, which is equivalent to Spin(7)-instantons on a cylinder over them. For a general SU(3)-equivariant gauge connection, the generalized instanton equations turn into gradient-flow equations on C^3 x R^2, with a particular cubic superpotential. For the simplest member of the Aloff-Wallach family (with 3-Sasakian structure) we present an explicit instanton solution of tanh-like shape.Comment: 1+17 pages, 1 figur

Kontexte, Theorien und Inhalte der Themen - Ergebnisse eine Expertenbefragung

In diesem Beitrag wird ein Überblick über die aktuellen Forschungsbereiche zu den Themenfeldern Granulare Materie, Dissipative Strukturbildung und Selbstorganisation gegeben. Dabei wird unterschieden in Forschungsbereiche, die Modelle und Theorien umfassen, sowie in konkrete Kontexte, die sich auf Anwendungen und Phänomene beziehen. Diese Ergebnisse basieren auf einer Expertenbefragung

experimentelle Untersuchung von adhäsiven Haftpads

Der Beitrag beschreibt, wie ein Haftpad (auch bekannt als Anti-Rutsch-Pad oder Klebepad) in Bezug auf seine Haftkraft sowie die Mechanismen seiner Haftung untersucht werden kann. Dabei werden verschiedener Experimente und (Rasterkraft-) mikroskopische Untersuchungen vorgestellt. Es zeigt sich, dass eine experimentelle Bestimmung der Haftkraft schwierig ist, da sie von sehr vielen Parametern abhängt. Die Messunsicherheiten sind daher groß. Die maximale Haftkraft liegt im Bereich von 20 N/cm² (Plexiglas) bzw. 10 N/cm² (Aluminium). Die Untersuchungen legen den Schluss nahe, dass für die Haftung einerseits der Luftdruck und andererseits die van-der-Waals-Kräfte ursächlich sind und beide in vergleichbarer Größenordnung liegen. Über die experimentellen Erkenntnisse hinausgehend wird auch eine mögliche Eignung des Haft-pads als Thema für den Physikunterricht diskutiert. Dafür spricht, dass das Thema authentisch und anspruchsvoll ist und Raum für unterschiedliche Lösungswege bietet. Bei der unterrichtlichen Umsetzungen sollten aber die großen Messunsicherheiten und die Schwierigkeit eines stabilen experimentellen Aufbaus mit bedacht werden