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

Remarks on E11 approach

We consider a few topics in $E_{11}$ approach to superstring/M-theory: even subgroups ($Z_2$ orbifolds) of $E_{n}$, n=11,10,9 and their connection to Kac-Moody algebras; $EE_{11}$ subgroup of $E_{11}$ and coincidence of one of its weights with the $l_1$ weight of $E_{11}$, known to contain brane charges; possible form of supersymmetry relation in $E_{11}$; decomposition of $l_1$ w.r.t. the $SO(10,10)$ and its square root at first few levels; particle orbit of $l_1 \ltimes E_{11}$. Possible relevance of coadjoint orbits method is noticed, based on a self-duality form of equations of motion in $E_{11}$.Comment: Two references adde

E11, generalised space-time and equations of motion in four dimensions

We construct the non-linear realisation of the semi-direct product of E11 and its first fundamental representation at low levels in four dimensions. We include the fields for gravity, the scalars and the gauge fields as well as the duals of these fields. The generalised space-time, upon which the fields depend, consists of the usual coordinates of four dimensional space-time and Lorentz scalar coordinates which belong to the 56-dimensional representation of E7. We demand that the equations of motion are first order in derivatives of the generalised space-time and then show that they are essentially uniquely determined by the properties of the E11 Kac-Moody algebra and its first fundamental representation. The two lowest equations correctly describe the equations of motion of the scalars and the gauge fields once one takes the fields to depend only on the usual four dimensional space-time

Voyager 1 imaging and IRIS observations of Jovian methane absorption and thermal emission: Implications for cloud structure

Images from three filters of the Voyager 1 wide angle camera are used to measure the continuum reflectivity and spectral gradient near 6000 A and the 6190 A band methane/continuum ratio for a variety of cloud features in Jupiter's atmosphere. The dark barge features in the North Equatorial Belt have anomalously strong positive continuum spectral gradients suggesting unique composition. Methane absorption is shown at unprecedented spatial scales for the Great Red Spot and its immediate environment, for a dark barge feature in the North Equatorial Belt, and for two hot spot and plume regions in the North Equatorial Belt. Methane absorption and five micrometer emission are correlated in the vicinity of the Great Red Spot but are anticorrelated in one of the plume hot spot regions. Methane absorption and simultaneous maps of five micrometer brightness temperature is quantitatively compared to realistic cloud structure models which include multiple scattering at five micrometer as well as in the visible. Variability in H2 quadrupole lines are also investigated

E_{11}, ten forms and supergravity

We extend the previously given non-linear realisation of E_{11} for the decomposition appropriate to IIB supergravity to include the ten forms that were known to be present in the adjoint representation. We find precise agreement with the results on ten forms found by closing the IIB supersymmetry algebra.Comment: 14 page

The E_{11} origin of all maximal supergravities

Starting from the eleven dimensional E_{11} non-linear realisation of M-theory we compute all possible forms, that is objects with totally antisymmetrised indices, that occur in four dimensions and above as well as all the 1-forms and 2-forms in three dimensions. In any dimension D, the D-1-forms lead to maximal supergravity theories with cosmological constants and they are in precise agreement with the patterns of gauging found in any dimension using supersymmetry. The D-forms correspond to the presence of space-filling branes which are crucial for the consistency of orientifold models and have not been derived from an alternative approach, with the exception of the 10-dimensional case. It follows that the gaugings of supergravities and the spacetime-filling branes possess an eleven dimensional origin within the E_{11} formulation of M-theory. This and previous results very strongly suggest that all the fields in the adjoint representation of E_{11} have a physical interpretation.Comment: 54 page

Little Groups of Preon Branes

Little groups for preon branes (i.e. configurations of branes with maximal (n-1)/n fraction of survived supersymmetry) for dimensions d=2,3,...,11 are calculated for all massless, and partially for massive orbits. For massless orbits little groups are semidirect product of d-2 translational group $T_{d-2}$ on a subgroup of (SO(d-2) $\times$ R-invariance) group. E.g. at d=9 the subgroup is exceptional $G_2$ group. It is also argued, that 11d Majorana spinor invariants, which distinguish orbits, are actually invariant under d=2+10 Lorentz group. Possible applications of these results include construction of field theories in generalized space-times with brane charges coordinates, different problems of group's representations decompositions, spin-statistics issues.Comment: LaTeX, 11 page

Zero differential resistance in two-dimensional electron systems at large filling factors

We report on a state characterized by a zero differential resistance observed in very high Landau levels of a high-mobility two-dimensional electron system. Emerging from a minimum of Hall field-induced resistance oscillations at low temperatures, this state exists over a continuous range of magnetic fields extending well below the onset of the Shubnikov-de Haas effect. The minimum current required to support this state is largely independent on the magnetic field, while the maximum current increases with the magnetic field tracing the onset of inter-Landau level scattering

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