E_11 and M Theory

We argue that eleven dimensional supergravity can be described by a non-linear realisation based on the group E_{11}. This requires a formulation of eleven dimensional supergravity in which the gravitational degrees of freedom are described by two fields which are related by duality. We show the existence of such a description of gravity.Comment: 21 pages, some typos corrected and two references adde

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

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

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

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

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

Vanishing Hall Resistance at High Magnetic Field in a Double Layer Two-Dimensional Electron System

At total Landau level filling factor $\nu_{tot}=1$ a double layer two-dimensional electron system with small interlayer separation supports a collective state possessing spontaneous interlayer phase coherence. This state exhibits the quantized Hall effect when equal electrical currents flow in parallel through the two layers. In contrast, if the currents in the two layers are equal, but oppositely directed, both the longitudinal and Hall resistances of each layer vanish in the low temperature limit. This finding supports the prediction that the ground state at $\nu_{tot}=1$ is an excitonic superfluid.Comment: 4 pages, 4 figure

Performance of Sentinel-2 NDVI for assessing the relationship between vegetation and soil moisture under extreme drought conditions

Initial indications are that the enhanced spatial and spectral resolution of Sentinel-2 would allow for better assess- ment of vegetation condition, and consequently improved application in conditions of moisture deficit/drought. Although NDVI and other indices are well established methods in drought monitoring, particularly at larger scales, little research has examined the suitability of Sentinel-2. While the utility of Landsat-8 NDVI in revealing local scale plant-soil dynamics has been explored, challenges around resolution have emerged. The principal aim of this study was to determine the extent to which NDVI time series reflects soil moisture conditions, and whether this offers an improvement over Landsat-8. On the basis of exposure to drought over the study period (Jul 2015-Mar 2017), availability of cloud-free imagery and measured soil moisture, five sites in South-Western United States were selected. These sites, normally dry to arid, were classified as being in various states of drought, but in general this represented extension and recession of a significant drought event. A secondary focus of the paper therefore was the performance of Sentinel-2 NDVI under extreme conditions. As far as we are aware, this represents the first study of this kind using Sentinel-2. Following supervised classification, NDVI time series for areas of 1km radius around the monitoring sta- tions were calculated. Sentinel-2 NDVI variants were calculated using Bands 8 (10m), 5, 6, 7, and 8A (20m). Landsat-8 NDVI was calculated at 30m resolution. Pearson correlation analysis was undertaken of all NDVI time series against soil moisture at all measured soil depths. In order to assess the difference in correlation strength produced from using the Sentinel-2 red-edge bands, compared to the standard NIR band, a principal component analysis (PCA) was conducted. This was performed on the combination of all Sentinel-2 bands and the combination of the red-edge bands. Performance of the Sentinel-2 red-edge NDVI time series against the standard NIR band was also evaluated using a Steiger comparison test. While no significant correlations between Landsat-8 NDVI and measured soil moisture were found, high significant correlations were present between moisture at depths of <30cm and Sentinel-2 NDVI at three sites. No significant positive correlations were found at two sites, despite similar conditions to the others. These sites were characterised by much lower vegetation cover, suggesting a minimum cover threshold of ≈30-40% is required. The PCA shows that at all sites of significant positive moisture-NDVI correlations, the linear combination of the red-edge bands produced stronger correlations than the poorer spectral, but higher spatial resolution band. NDVI calculated using the higher spectral resolution bands may therefore be of greater use in this context than the higher spatial resolution option. However, each site/measurement with a relationship present also had an individual component which out-performed the PCA combination, most likely related to the spectral characteristics of local vegetation. These results suggest high potential for the application of Sentinel-2 NDVI in drought monitoring, even in extreme environments, thus allowing us to further our understanding of local scale plant-soil dynamics under such conditions

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