Lie-Poisson groups and the Miura transformation

We point out that the recent proof of the Kupershmidt-Wilson theorem by Cheng and Mas-Ramos is underpinned by the Lie-Poisson property of the second Gel'fand-Dickey bracket. The supersymmetric Kupershmidt-Wilson theorem is also proved along these same lines. Finally we comment on the possible repercussions in the problem of the coproduct for W-algebras.Comment: .dvi file, uses AMSFonts 2.1+, 10 pages (5 physical pages in landscape mode), no figure

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

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

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

Half-BPS quotients in M-theory: ADE with a twist

We classify Freund-Rubin backgrounds of eleven-dimensional supergravity of the form AdS_4 x X^7 which are at least half BPS; equivalently, smooth quotients of the round 7-sphere by finite subgroups of SO(8) which admit an (N>3)-dimensional subspace of Killing spinors. The classification is given in terms of pairs consisting of an ADE subgroup of SU(2) and an automorphism defining its embedding in SO(8). In particular we find novel half-BPS quotients associated with the subgroups of type D_n (for n>5), E_7 and E_8 and their outer automorphisms.Comment: 16 pages; V2: notational inconsistencies addressed, final version to be published in JHE

A geometric construction of the exceptional Lie algebras F4 and E8

We present a geometric construction of the exceptional Lie algebras F4 and E8 starting from the round 8- and 15-spheres, respectively, inspired by the construction of the Killing superalgebra of a supersymmetric supergravity background. (There is no supergravity in the paper.)Comment: 12 page

Groups and the Entropy Floor- XMM-Newton Observations of Two Groups

Using XMM-Newton spatially resolved X-ray imaging spectroscopy we obtain the temperature, density, entropy, gas mass, and total mass profiles for two groups of galaxies out to ~0.3 Rvir (Rvir, the virial radius). Our density profiles agree well with those derived previously, and the temperature data are broadly consistent with previous results but are considerably more precise. Both of these groups are at the mass scale of 2x10^13 Msolar but have rather different properties. They have considerably lower gas mass fractions at r<0.3 Rvir than the rich clusters. NGC2563, one of the least luminous groups for its X-ray temperature, has a very low gas mass fraction of ~0.004 inside 0.1 Rvir, which rises with radius. NGC4325, one of the most luminous groups at the same average temperature, has a higher gas mass fraction of 0.02. The entropy profiles and the absolute values of the entropy as a function of virial radius also differ, with NGC4325 having a value of ~100 keV cm-2 and NGC2563 a value of ~300 keV cm-2 at r~0.1 Rvir. For both groups the profiles rise monotonically with radius and there is no sign of an entropy "floor". These results are inconsistent with pre-heating scenarios which have been developed to explain the entropy floor in groups but are broadly consistent with models of structure formation which include the effects of heating and/or the cooling of the gas. The total entropy in these systems provides a strong constraint on all models of galaxy and group formation, and on the poorly defined feedback process which controls the transformation of gas into stars and thus the formation of structure in the universe.Comment: 22 pages, 2 figure