26,034 research outputs found
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
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
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
Intersection Graph of a Module
Let be a left -module where is a (not necessarily commutative)
ring with unit. The intersection graph \cG(V) of proper -submodules of
is an undirected graph without loops and multiple edges defined as follows: the
vertex set is the set of all proper -submodules of and there is an edge
between two distinct vertices and if and only if We
study these graphs to relate the combinatorial properties of \cG(V) to the
algebraic properties of the -module We study connectedness, domination,
finiteness, coloring, and planarity for \cG (V). For instance, we find the
domination number of \cG (V). We also find the chromatic number of \cG(V)
in some cases. Furthermore, we study cycles in \cG(V), and complete subgraphs
in \cG (V) determining the structure of for which \cG(V) is planar
Remarks on E11 approach
We consider a few topics in approach to superstring/M-theory: even
subgroups ( orbifolds) of , n=11,10,9 and their connection to
Kac-Moody algebras; subgroup of and coincidence of one of
its weights with the weight of , known to contain brane charges;
possible form of supersymmetry relation in ; decomposition of
w.r.t. the and its square root at first few levels; particle orbit
of . Possible relevance of coadjoint orbits method is
noticed, based on a self-duality form of equations of motion in .Comment: Two references adde
A FUSE survey of high-latitude Galactic molecular hydrogen
Measurements of molecular hydrogen (H_2) column densities are presented for
the first six rotational levels (J=0 to 5) for 73 extragalactic targets
observed with FUSE. All of these have a final signal-to-noise ratio larger than
\snlimit, and are located at galactic latitude |b|>20 deg. The individual
observations were calibrated with the FUSE calibration pipeline CalFUSE version
2.1 or higher, and then carefully aligned in velocity. The final velocity
shifts for all the FUSE segments are listed. H_2 column densities or limits are
determined for the 6 lowest rotational (J) levels for each HI component in the
line of sight, using a curve-of-growth approach at low column densities ~16.5),
and Voigt-profile fitting at higher column densities. Detections include 73
measurements of low-velocity H_2 in the Galactic Disk and lower Halo. Eight
sightlines yield non-detections for Galactic H_2. The measured column densities
range from log N(H_2)=14 to log N(H_2)=20. Strong correlations are found
between log N(H_2) and T_01, the excitation temperature of the H_2, as well as
between log N(H_2) and the level population ratios (log (N(J')/N(J))). The
average fraction of nuclei in molecular hydrogen (f(H_2)) in each sightline is
calculated; however, because there are many HI clouds in each sightline, the
physics of the transition from HI to H_2 can not be studied. Detections also
include H2 in 16 intermediate-velocity clouds in the Galactic Halo (out of 35
IVCs). Molecular hydrogen is seen in one high-velocity cloud (the Leading Arm
of the Magellanic Stream), although 19 high-velocity clouds are intersected;
this strongly suggests that dust is rare or absent in these objects. Finally,
there are five detections of H_2 in external galaxies.Comment: Accepted for ApJ Supplement. Note: figs 7 and 8 not included because
astro-ph rejects them as too bi
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
The Low-level Spectrum of the String
We investigate the spectrum of physical states in the string theory, up
to level 2 for a multi-scalar string, and up to level 4 for the two-scalar
string. The (open) string has a photon as its only massless state. By
using screening charges to study the null physical states in the two-scalar
string, we are able to learn about the gauge symmetries of the states in
the multi-scalar string.Comment: 31 pages, Plain Tex, CTP TAMU-70/92, Goteborg ITP 92-43,
Imperial/TP/91-92/22, KCL-TH-92-
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