An E9 multiplet of BPS states

We construct an infinite E9 multiplet of BPS states for 11D supergravity. For each positive real root of E9 we obtain a BPS solution of 11D supergravity, or of its exotic counterparts, depending on two non-compact transverse space variables. All these solutions are related by U-dualities realised via E9 Weyl transformations in the regular embedding of E9 in E10, E10 in E11. In this way we recover the basic BPS solutions, namely the KK-wave, the M2 brane, the M5 brane and the KK6-monopole, as well as other solutions admitting eight longitudinal space dimensions. A novel technique of combining Weyl reflexions with compensating transformations allows the construction of many new BPS solutions, each of which can be mapped to a solution of a dual effective action of gravity coupled to a certain higher rank tensor field. For real roots of E10 which are not roots of E9, we obtain additional BPS solutions transcending 11D supergravity (as exemplified by the lowest level solution corresponding to the M9 brane). The relation between the dual formulation and the one in terms of the original 11D supergravity fields has significance beyond the realm of BPS solutions. We establish the link with the Geroch group of general relativity, and explain how the E9 duality transformations generalize the standard Hodge dualities to an infinite set of `non-closing dualities'.Comment: 76 pages, 6 figure

Finite and infinite-dimensional symmetries of pure N=2 supergravity in D=4

We study the symmetries of pure N=2 supergravity in D=4. As is known, this theory reduced on one Killing vector is characterised by a non-linearly realised symmetry SU(2,1) which is a non-split real form of SL(3,C). We consider the BPS brane solutions of the theory preserving half of the supersymmetry and the action of SU(2,1) on them. Furthermore we provide evidence that the theory exhibits an underlying algebraic structure described by the Lorentzian Kac-Moody group SU(2,1)^{+++}. This evidence arises both from the correspondence between the bosonic space-time fields of N=2 supergravity in D=4 and a one-parameter sigma-model based on the hyperbolic group SU(2,1)^{++}, as well as from the fact that the structure of BPS brane solutions is neatly encoded in SU(2,1)^{+++}. As a nice by-product of our analysis, we obtain a regular embedding of the Kac-Moody algebra su(2,1)^{+++} in e_{11} based on brane physics.Comment: 70 pages, final version published in JHE

Hidden Symmetries and Dirac Fermions

In this paper, two things are done. First, we analyze the compatibility of Dirac fermions with the hidden duality symmetries which appear in the toroidal compactification of gravitational theories down to three spacetime dimensions. We show that the Pauli couplings to the p-forms can be adjusted, for all simple (split) groups, so that the fermions transform in a representation of the maximal compact subgroup of the duality group G in three dimensions. Second, we investigate how the Dirac fermions fit in the conjectured hidden overextended symmetry G++. We show compatibility with this symmetry up to the same level as in the pure bosonic case. We also investigate the BKL behaviour of the Einstein-Dirac-p-form systems and provide a group theoretical interpretation of the Belinskii-Khalatnikov result that the Dirac field removes chaos.Comment: 30 page

G2 Dualities in D=5 Supergravity and Black Strings

Five dimensional minimal supergravity dimensionally reduced on two commuting Killing directions gives rise to a G2 coset model. The symmetry group of the coset model can be used to generate new solutions by applying group transformations on a seed solution. We show that on a general solution the generators belonging to the Cartan and nilpotent subalgebras of G2 act as scaling and gauge transformations, respectively. The remaining generators of G2 form a sl(2,R)+sl(2,R) subalgebra that can be used to generate non-trivial charges. We use these generators to generalize the five dimensional Kerr string in a number of ways. In particular, we construct the spinning electric and spinning magnetic black strings of five dimensional minimal supergravity. We analyze physical properties of these black strings and study their thermodynamics. We also explore their relation to black rings.Comment: typos corrected (26 pages + appendices, 2 figures

A successful model for the evolution of the FID signal with motion

We discuss the shape of the nuclear FID for motions of intermediate rate, whereby the dipolar interactions are averaged to zero. A simple model described here, has provided a very good account of the variation of the FID shape with temperature for a single crystal. In this article we analyze the same model for a powder. Experiments in a powder of hexamethylethane are described and compared with those of a simple crystal

Target-dependent regulation of acetylcholine secretion at developing motoneurons in Xenopus cell cultures

Myocyte-dependent regulation of acetylcholine (ACh) quantal secretion from developing motoneurons was studied in day-3 Xenopus nerve-muscle co-cultures. Spontaneous synaptic currents (SSCs) were measured in manipulated synapses by using whole-cell voltage-clamped myocytes. Changes in SSC amplitude were assumed to reflect changes in the ACh content of secreted quantal packets. Compared with natural synapses, motoneurons without any contact with a myocyte (naive neurons) released ACh in smaller quantal packets.Bipolar cultured motoneurons, which were in contact with a myocyte with one axon branch (contact-end) but remained free at another axon branch (free-end), were further used to examine quantal ACh secretion. The ACh quantal size recorded at free-end terminals was similar to that of naive neurons and was smaller than that at the contact-end, indicating that myocyte contact exerts differential regulation on quantal secretion in the same neuron.Some of the neurons that formed a natural synapse with a myocyte continued to grow forward and ACh quantal secretion from the free growth cone was examined. The ACh quantal size recorded at free growth cones was inversely proportional to the distance to the natural synapse, implying localized regulation of quantal secretion by the myocyte.Chronic treatment of day-1 cultures with veratridine and d-tubocurarine, respectively, increased and decreased the neurotrophic action of myocytes when assayed on day 3.Taken together, these findings suggest that the myocyte is an important postsynaptic target in the regulation of quantal secretion and that the trophic action is spatially restricted to the neighbourhood of the neuromuscular junction