Representations of G+++ and the role of space-time

We consider the decomposition of the adjoint and fundamental representations of very extended Kac-Moody algebras G+++ with respect to their regular A type subalgebra which, in the corresponding non-linear realisation, is associated with gravity. We find that for many very extended algebras almost all the A type representations that occur in the decomposition of the fundamental representations also occur in the adjoint representation of G+++. In particular, for E8+++, this applies to all its fundamental representations. However, there are some important examples, such as An+++, where this is not true and indeed the adjoint representation contains no generator that can be identified with a space-time translation. We comment on the significance of these results for how space-time can occur in the non-linear realisation based on G+++. Finally we show that there is a correspondence between the A representations that occur in the fundamental representation associated with the very extended node and the adjoint representation of G+++ which is consistent with the interpretation of the former as charges associated with brane solutions.Comment: 45 pages, 9 figures, 9 tables, te

Giant microwave photoresistivity in a high-mobility quantum Hall system

We report the observation of a remarkably strong microwave photoresistivity effect in a high-mobility two-dimensional electron system subject to a weak magnetic field and low temperature. The effect manifests itself as a giant microwave-induced resistivity peak which, in contrast to microwave-induced resistance oscillations, appears only near the second harmonic of the cyclotron resonance and only at sufficiently high microwave frequencies. Appearing in the regime linear in microwave intensity, the peak can be more than an order of magnitude stronger than the microwave-induced resistance oscillations and cannot be explained by existing theories.Comment: 4 pages, 4 figure

Very Extended E8E_8 and A8A_8 at low levels, Gravity and Supergravity

We define a level for a large class of Lorentzian Kac-Moody algebras. Using this we find the representation content of very extended $A_{D-3}$ and $E_8$ (i.e. $E_{11}$) at low levels in terms of $A_{D-1}$ and $A_{10}$ representations respectively. The results are consistent with the conjectured very extended $A_8$ and $E_{11}$ symmetries of gravity and maximal supergravity theories given respectively in hep-th/0104081 and hep-th/0107209. We explain how these results provided further evidence for these conjectures.Comment: 16 pages, plain tex (equation 3.3 modified and one reference expanded

Temperature Dependence of Microwave Photoresistance in 2D Electron Systems

We report on the temperature dependence of microwave-induced resistance oscillations in high-mobility two-dimensional electron systems. We find that the oscillation amplitude decays exponentially with increasing temperature, as $\exp(-\alpha T^2)$, where $\alpha$ scales with the inverse magnetic field. This observation indicates that the temperature dependence originates primarily from the modification of the single particle lifetime, which we attribute to electron-electron interaction effects.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Let

Generalised geometry, eleven dimensions and E11

We construct the non-linear realisation of E11 and its first fundamental representation in eleven dimensions at low levels. The fields depend on the usual coordinates of space-time as well as two form and five form coordinates. We derive the terms in the dynamics that contain the three form and six form fields and show that when we restricted their field dependence to be only on the usual space-time we recover the correct self-duality relation. Should this result generalise to the gravity fields then the non-linear realisation is an extension of the maximal supergravity theory, as previously conjectured. We also comment on the connections between the different approaches to generalised geometry.Comment: 17 pages, Trivial typos corrected in version one and a substantial note added which gives the equation of motion relating the gravity field to its dua

HypTrails: A Bayesian Approach for Comparing Hypotheses About Human Trails on the Web

When users interact with the Web today, they leave sequential digital trails on a massive scale. Examples of such human trails include Web navigation, sequences of online restaurant reviews, or online music play lists. Understanding the factors that drive the production of these trails can be useful for e.g., improving underlying network structures, predicting user clicks or enhancing recommendations. In this work, we present a general approach called HypTrails for comparing a set of hypotheses about human trails on the Web, where hypotheses represent beliefs about transitions between states. Our approach utilizes Markov chain models with Bayesian inference. The main idea is to incorporate hypotheses as informative Dirichlet priors and to leverage the sensitivity of Bayes factors on the prior for comparing hypotheses with each other. For eliciting Dirichlet priors from hypotheses, we present an adaption of the so-called (trial) roulette method. We demonstrate the general mechanics and applicability of HypTrails by performing experiments with (i) synthetic trails for which we control the mechanisms that have produced them and (ii) empirical trails stemming from different domains including website navigation, business reviews and online music played. Our work expands the repertoire of methods available for studying human trails on the Web.Comment: Published in the proceedings of WWW'1

Duality Symmetries and G^{+++} Theories

We show that the non-linear realisations of all the very extended algebras G^{+++}, except the B and C series which we do not consider, contain fields corresponding to all possible duality symmetries of the on-shell degrees of freedom of these theories. This result also holds for G_2^{+++} and we argue that the non-linear realisation of this algebra accounts precisely for the form fields present in the corresponding supersymmetric theory. We also find a simple necessary condition for the roots to belong to a G^{+++} algebra.Comment: 35 pages. v2: 2 appendices added, other minor corrections. v3: tables corrected, other minor changes, one appendix added, refs. added. Version published in Class. Quant. Gra

Gradient Representations and Affine Structures in AE(n)

We study the indefinite Kac-Moody algebras AE(n), arising in the reduction of Einstein's theory from (n+1) space-time dimensions to one (time) dimension, and their distinguished maximal regular subalgebras sl(n) and affine A_{n-2}^{(1)}. The interplay between these two subalgebras is used, for n=3, to determine the commutation relations of the `gradient generators' within AE(3). The low level truncation of the geodesic sigma-model over the coset space AE(n)/K(AE(n)) is shown to map to a suitably truncated version of the SL(n)/SO(n) non-linear sigma-model resulting from the reduction Einstein's equations in (n+1) dimensions to (1+1) dimensions. A further truncation to diagonal solutions can be exploited to define a one-to-one correspondence between such solutions, and null geodesic trajectories on the infinite-dimensional coset space H/K(H), where H is the (extended) Heisenberg group, and K(H) its maximal compact subgroup. We clarify the relation between H and the corresponding subgroup of the Geroch group.Comment: 43 page

Observation of exchange Coulomb interactions in the quantum Hall state at nu=3

Coulomb exchange interactions of electrons in the nu=3 quantum Hall state are determined from two inter-Landau level spin-flip excitations measured by resonant inelastic light scattering. The two coupled collective excitations are linked to inter-Landau level spin-flip transitions arising from the N=0 and N=1 Landau levels. The strong repulsion between the two spin-flip modes in the long-wave limit is clearly manifested in spectra displaying Coulomb exchange contributions that are comparable to the exchange energy for the quantum Hall state at nu=1. Theoretical calculations within the Hartree-Fock approximation are in a good agreement with measured energies of spin-flip collective excitations.Comment: 5 pages, 3 figures, to appear in PRB Rapid Communication

E_{11} origin of Brane charges and U-duality multiplets

We derive general equations which determine the decomposition of the G^{+++} multiplet of brane charges into the sub-algebras that arise when the non-linearly realised G^{+++} theory is dimensionally reduced on a torus. We apply this to calculate the low level E_8 multiplets of brane charges that arise when the E_{8}^{+++}, or E_{11}, non-linearly realised theory is dimensionally reduced to three dimensions on an eight dimensional torus. We find precise agreement with the U-duality multiplet of brane charges previously calculated, thus providing a natural eleven dimensional origin for the "mysterious" brane charges found that do not occur as central charges in the supersymmetry algebra. We also discuss the brane charges in nine dimensions and how they arise from the IIA and IIB theories.Comment: 30 pages, plain te