Missing Modules, the Gnome Lie Algebra, and E10E_{10}

We study the embedding of Kac-Moody algebras into Borcherds (or generalized Kac-Moody) algebras which can be explicitly realized as Lie algebras of physical states of some completely compactified bosonic string. The extra ``missing states'' can be decomposed into irreducible highest or lowest weight ``missing modules'' w.r.t. the relevant Kac-Moody subalgebra; the corresponding lowest weights are associated with imaginary simple roots whose multiplicities can be simply understood in terms of certain polarization states of the associated string. We analyse in detail two examples where the momentum lattice of the string is given by the unique even unimodular Lorentzian lattice $II_{1,1}$ or $II_{9,1}$, respectively. The former leads to the Borcherds algebra $g_{1,1}$, which we call ``gnome Lie algebra", with maximal Kac-Moody subalgebra $A_1$. By the use of the denominator formula a complete set of imaginary simple roots can be exhibited, whereas the DDF construction provides an explicit Lie algebra basis in terms of purely longitudinal states of the compactified string in two dimensions. The second example is the Borcherds algebra $g_{9,1}$, whose maximal Kac-Moody subalgebra is the hyperbolic algebra $E_{10}$. The imaginary simple roots at level 1, which give rise to irreducible lowest weight modules for $E_{10}$, can be completely characterized; furthermore, our explicit analysis of two non-trivial level-2 root spaces leads us to conjecture that these are in fact the only imaginary simple roots for $g_{9,1}$.Comment: 31 pages, LaTeX2e, AMS packages, PSTRICK

Explicit determination of a 727-dimensional root space of the hyperbolic Lie algebra E10E_{10}

The 727-dimensional root space associated with the level-2 root \bLambda_1 of the hyperbolic Kac--Moody algebra $E_{10}$ is determined using a recently developed string theoretic approach to hyperbolic algebras. The explicit form of the basis reveals a complicated structure with transversal as well as longitudinal string states present.Comment: 12 pages, LaTeX 2

E10 and a "small tension expansion" of M Theory

A formal ``small tension'' expansion of D=11 supergravity near a spacelike singularity is shown to be equivalent, at least up to 30th order in height, to a null geodesic motion in the infinite dimensional coset space E10/K(E10) where K(E10) is the maximal compact subgroup of the hyperbolic Kac-Moody group E10(R). For the proof we make use of a novel decomposition of E10 into irreducible representations of its SL(10,R) subgroup. We explicitly show how to identify the first four rungs of the E10 coset fields with the values of geometric quantities constructed from D=11 supergravity fields and their spatial gradients taken at some comoving spatial point.Comment: 4 page

(2,0) Supersymmetry and the Light-Cone Description of M5-branes

In 1007.2982 a novel system of equations which propagate in one null and four space directions were obtained as the on-shell conditions for the six-dimensional (2,0) superalgebra. In this paper we show how this system reduces to one-dimensional motion on instanton moduli space. Quantization leads to the previous light-cone proposal of the (2,0) theory, generalized to include a potential that arises on the Coulomb branch as well as couplings to background gauge and self-dual two-form fields.Comment: 15 pages, v2: minor clarifications to sections 3 and 5, references added. This version to appear in JHE

Electrified branes

A geometrical form of the supersymmetry conditions for D-branes on arbitrary type II supersymmetric backgrounds is derived, as well as the associated BPS bounds. The treatment is general and allows to consider, for instance, non-static configurations or D-branes supporting a non-vanishing electric flux, hence completing previous partial results. In particular, our discussion clarifies how the notion of calibration can be extended in order to be applicable to the most general supersymmetric configurations. As an exemplifying preliminary step, the procedure followed is first applied to fundamental strings.Comment: 36 page

Borcherds Algebras and N=4 Topological Amplitudes

The perturbative spectrum of BPS-states in the E_8 x E_8 heterotic string theory compactified on T^2 is analysed. We show that the space of BPS-states forms a representation of a certain Borcherds algebra G which we construct explicitly using an auxiliary conformal field theory. The denominator formula of an extension G_{ext} \supset G of this algebra is then found to appear in a certain heterotic one-loop N=4 topological string amplitude. Our construction thus gives an N=4 realisation of the idea envisioned by Harvey and Moore, namely that the `algebra of BPS-states' controls the threshold corrections in the heterotic string.Comment: 39 page

Onboard autonomy and fault protection concept of the BIRD satellite

BIRD (Bi-Spectral Infra-Red Detection) has been demonstrating new technologies since its launch on 22 October, 2001. Besides the successful in-orbit test of the detection and evaluation of vegetation fires with micro satellites, BIRD has also been demonstrating a number of advanced spacecraft bus technologies, especially in the field of satellite autonomy and fault detection and protection. A number of ingenious features make it possible to operate the 92 kg satellite in a comfortable and safely way. Special features include the autonomous management of onboard computer failures, surveillance and response to critical parameters limit exceeding, system attitude anomalies. A robust redundancy philosophy and optimized ground-spacecraft interaction concept has contributed to the success of the BIRD mission, which was designed to operate for one year and has completed now its second year of operation. The paper describes the related new technologies and the results from the experience with BIRD

Technology Demonstration by the BIRD Mission

The micro satellite mission BIRD demonstrates the technical and programmatic feasibility of the combination of ambitious science and new, not yet space-proven advanced technologies under fixed budget constraints. The demonstration of new micro satellite technologies is one key point of the BIRD mission. The technology experiments demonstrate the limits and the advantages of the new developed components and technologies. The micro satellite BIRD (mass = 92kg) was launched with the Indian PSLV-C3 from Shar on 22 October, 2001 into an Sun-synchronous circular orbit at an altitude of about 568km. The paper describes the new developed technologies and the results of the space demonstration

Technologiedemonstration mit dem DLR-Kleinsatelliten BIRD

In der DLR-Kleinsatellitenmission BIRD wird eine neue Generation von gekühlten Infrarotsensoren im Orbit zur Fernerkundung der Erde eingesetzt. Aus den Missionsrandbedingungen bestand die Grundforderung, dass die Missionsziele im Rahmen einer Mikrosatelliten-Mission erreicht werden müssen, d.h. mit einem Satelliten der 100kg-Klasse, der gemeinsam mit einem größeren Satelliten in den Orbit mitgenommen werden kann. Dies stellte hohe Anforderungen an den Satellitenbus, die mit einer Reihe innovativer technologischer Lösungen in einem engen Kostenrahmen erfüllt wurden. Wesentliche Merkmale des BIRD-Satellitenbusses sind: - Mikrosatellitenstruktur mit hoher mechanischer Stabilität in Kompaktbauweise, die an verschiedene Mitstart-Plattformen anpassbar ist, - Bus-Nutzlast-Masseverhältnis = 64 kg : 30 kg, - Hoher Spitzenleistungsumsatz von 200W für ca. 10 bis 20 min bei einem mittleren Leistungsumsatz von ca. 60 W - Modernes (im wesentlichen) passives Thermalkontrollsystem mit Radiatoren, Wärmrohre, Temperaturfühler und Notheizer), - Neu entwickelter Hochleistungsbordrechner (4fache Ausführung) mit integriertem Latch-up-Schutz und Fehlererkennungs- und -korrektursystem, - Lageregelung im Zustandsraum mit neu entwickelten Präzisionsdrallrädern und neu entwickelter Sternkamera, - Hochgenaues An-Bord-Navigationssystem auf Basis von GPS-Daten (5 m Genauigkeit nachgewiesen), - S-Band Kommunikation in hoher (2 Mbps) und niedriger Bitrate für Kommando- und Datenübertragung, - Redundantes an-Bord-Datensystem für die Nutzlast mit 1Gbit-Massenspeicher. Auf Seiten der Nutzlast ist nicht nur das Infrarotsystem Teil der Technologiedemonstration im Rahmen des BIRD-Programms, sondern auch ein an-Bord-Klassifikator auf der Basis eines künstlichen neuronalen Netzwerk-Chips. Mit diesem Experiment soll die Machbarkeit einer thematischen Datenverarbeitung an Bord eines Satelliten bis zu einem High-level-Datenprodukt demonstriert werden. In dem Vortrag sollen die Ziele der technologischen Experimente bzw. der Technologiedemonstrationen, die technischen Lösungen und die erreichten Ergebnisse vorgestellt werden

Technology demonstration by the BIRD-mission

The micro satellite mission BIRD demonstrates the technical and programmatic feasibility of the combination of ambitious science and new, not yet space-proven advanced technologies under fixed budget constraints. The demonstration of new micro satellite technologies is one key point of the BIRD mission. The technology experiments demonstrate the limits and the advantages of the new developed components and technologies. The micro satellite BIRD (mass = 92kg) was launched with the Indian PSLV-C3 from Shar on 22 October, 2001 into an Sun-synchronous circular orbit at an altitude of about 568km. The paper describes the new developed technologies and the results of the space demonstration