D-brane charge, flux quantisation and relative (co)homology

We reconsider the problem of U(1) flux and D0-charge for D-branes in the WZW model and investigate the relationship between the different definitions that have been proposed recently. We identify the D0-charge as a particular reduction of a class in the relative cohomology of the group modulo the D-submanifold. We investigate under which conditions this class is equivalent to the first Chern class of a line bundle on the D-submanifold and we find that in general there is an obstruction given by the cohomology class of the NS 3-form. Therefore we conclude that for topologically nontrivial B-fields, there is strictly speaking no U(1) gauge field on the D-submanifold. Nevertheless the ambiguity in the flux is not detected by the D0-charge. This has a natural interpretation in terms of gerbes.Comment: 16 pages, 3 figures (v2: cosmetic changes and definition of relative de Rham complex

New Supersymmetrizations of the Generalized KdV Hierarchies

Recently we investigated a new supersymmetrization procedure for the KdV hierarchy inspired in some recent work on supersymmetric matrix models. We extend this procedure here for the generalized KdV hierarchies. The resulting supersymmetric hierarchies are generically nonlocal, except for the case of Boussinesque which we treat in detail. The resulting supersymmetric hierarchy is integrable and bihamiltonian and contains the Boussinesque hierarchy as a subhierarchy. In a particular realization, we extend it by defining supersymmetric odd flows. We end with some comments on a slight modification of this supersymmetrization which yields local equations for any generalized KdV hierarchy.Comment: 10 pages, uuencoded compressed tar'd .dvi file, Bonn-HE-93-1

On the structure of symmetric self-dual Lie algebras

A finite-dimensional Lie algebra is called (symmetric) self-dual, if it possesses an invariant nondegenerate (symmetric) bilinear form. Symmetric self-dual Lie algebras have been studied by Medina and Revoy, who have proven a very useful theorem about their structure. In this paper we prove a refinement of their theorem which has wide applicability in Conformal Field Theory, where symmetric self-dual Lie algebras start to play an important role due to the fact that they are precisely the Lie algebras which admit a Sugawara construction. We also prove a few corollaries which are important in Conformal Field Theory. (This paper provides mathematical details of results used, but only sketched, in the companion paper hep-th/9506151.)Comment: 19 pages, .dvi.uu (needs AMSFonts 2.1+

CONSIDERATIONS REGARDING FISH FARMING IN POLYCULTURE SYSTEM

Marine aquaculture is becoming more widely recognized as a viable alternative to fishing for supplying high-quality protein to the world's rising population. Capture fisheries output is falling short of global demand, and yearly seafood consumption has increased by more than double in the previous three decades. Under these conditions, raising fish in a polyculture system could be a viable option for increasing production globally, but with low effects on the environment

Gauging the Wess-Zumino term of a sigma model with boundary

We investigate the gauging of the Wess-Zumino term of a sigma model with boundary. We derive a set of obstructions to gauging and we interpret them as the conditions for the Wess-Zumino term to extend to a closed form in a suitable equivariant relative de Rham complex. We illustrate this with the two-dimensional sigma model and we show that the new obstructions due to the boundary can be interpreted in terms of Courant algebroids. We specialise to the case of the Wess-Zumino-Witten model, where it is proved that there always exist suitable boundary conditions which allow gauging any subgroup which can be gauged in the absence of a boundary. We illustrate this with two natural classes of gaugings: (twisted) diagonal subgroups with boundary conditions given by (twisted) conjugacy classes, and chiral isotropic subgroups with boundary conditions given by cosets.Comment: 18 pages (minor changes in response to referee report

Clinical reasoning in feline epilepsy: Which combination of clinical information is useful?

We sought to identify the association between clinical risk factors and the diagnosis of idiopathic epilepsy (IE) or structural epilepsy (SE) in cats, using statistical models to identify combinations of discrete parameters from the patient signalment, history and neurological examination findings that could suggest the most likely diagnosis. Data for 138 cats with recurrent seizures were reviewed, of which 110 were valid for inclusion. Seizure aetiology was classified as IE in 57% and SE in 43% of cats. Binomial logistic regression analyses demonstrated that pedigree status, older age at seizure onset (particularly >7 years old), abnormal neurological examinations, and ictal vocalisation were associated with a diagnosis of SE compared to IE, and that ictal salivation was more likely to be associated with a diagnosis of IE than SE. These findings support the importance of considering inter-ictal neurological deficits and seizure history in clinical reasoning

Penrose limits of Lie Branes and a Nappi--Witten braneworld

Departing from the observation that the Penrose limit of AdS_3 x S^3 is a group contraction in the sense of Inonu and Wigner, we explore the relation between the symmetric D-branes of AdS_3 x S^3 and those of its Penrose limit, a six-dimensional symmetric plane wave analogous to the four-dimensional Nappi--Witten spacetime. Both backgrounds are Lie groups admitting bi-invariant lorentzian metrics and symmetric D-branes wrap their (twisted) conjugacy classes. We determine the (twisted and untwisted) symmetric D-branes in the plane wave background and we prove the existence of a space-filling D5-brane and, separately, of a foliation by D3-branes with the geometry of the Nappi--Witten spacetime which can be understood as the Penrose limit of the AdS_2 x S^2 D3-brane in AdS_3 x S^3. Parenthetically we also derive a simple criterion for a symmetric plane wave to be isometric to a lorentzian Lie group. In particular we observe that the maximally supersymmetric plane wave in IIB string theory is isometric to a lorentzian Lie group, whereas the one in M-theory is not.Comment: 21 pages (v2: references added