24,480 research outputs found
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
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
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
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
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
Sugawara-type constraints in hyperbolic coset models
In the conjectured correspondence between supergravity and geodesic models on
infinite-dimensional hyperbolic coset spaces, and E10/K(E10) in particular, the
constraints play a central role. We present a Sugawara-type construction in
terms of the E10 Noether charges that extends these constraints infinitely into
the hyperbolic algebra, in contrast to the truncated expressions obtained in
arXiv:0709.2691 that involved only finitely many generators. Our extended
constraints are associated to an infinite set of roots which are all imaginary,
and in fact fill the closed past light-cone of the Lorentzian root lattice. The
construction makes crucial use of the E10 Weyl group and of the fact that the
E10 model contains both D=11 supergravity and D=10 IIB supergravity. Our
extended constraints appear to unite in a remarkable manner the different
canonical constraints of these two theories. This construction may also shed
new light on the issue of `open constraint algebras' in traditional canonical
approaches to gravity.Comment: 49 page
Kac-Moody Symmetries of Ten-dimensional Non-maximal Supergravity Theories
A description of the bosonic sector of ten-dimensional N=1 supergravity as a
non-linear realisation is given. We show that if a suitable extension of this
theory were invariant under a Kac-Moody algebra, then this algebra would have
to contain a rank eleven Kac-Moody algebra, that can be identified to be a
particular real form of very-extended D_8. We also describe the extension of
N=1 supergravity coupled to an abelian vector gauge field as a non-linear
realisation, and find the Kac-Moody algebra governing the symmetries of this
theory to be very-extended B_8. Finally, we discuss the related points for the
N=1 supergravity coupled to an arbitrary number of abelian vector gauge fields
A Completely Invariant SUSY Transform of Supersymmetric QED
We study the SUSY breaking of the covariant gauge-fixing term in SUSY QED and
observe that this corresponds to a breaking of the Lorentz gauge condition by
SUSY. Reasoning by analogy with SUSY's violation of the Wess-Zumino gauge, we
argue that the SUSY transformation, already modified to preserve Wess-Zumino
gauge, should be further modified by another gauge transformation which
restores the Lorentz gauge condition. We derive this modification and use the
resulting transformation to derive a Ward identitiy relating the photon and
photino propagators without using ghost fields. Our transformation also
fulfills the SUSY algebra, modulo terms that vanish in Lorentz gauge
Spin and the Coulomb Gap in the Half-Filled Lowest Landau Level
The Coulomb gap observed in tunneling between parallel two-dimensional
electron systems, each at half filling of the lowest Landau level, is found to
depend sensitively on the presence of an in-plane magnetic field. Especially at
low electron density, the width of the Coulomb gap at first increases sharply
with in-plane field, but then abruptly levels off. This behavior appears to
coincide with the known transition from partial to complete spin polarization
of the half-filled lowest Landau level. The tunneling gap therefore opens a new
window onto the spin configuration of two-dimensional electron systems at high
magnetic field.Comment: 6 pages, 4 postscript figures. Minor changes. To appear in Physical
Review
Fermi surface of the colossal magnetoresistance perovskite La_{0.7}Sr_{0.3}MnO_{3}
Materials that exhibit colossal magnetoresistance (CMR) are currently the
focus of an intense research effort, driven by the technological applications
that their sensitivity lends them to. Using the angular correlation of photons
from electron-positron annihilation, we present a first glimpse of the Fermi
surface of a material that exhibits CMR, supported by ``virtual crystal''
electronic structure calculations. The Fermi surface is shown to be
sufficiently cubic in nature that it is likely to support nesting.Comment: 5 pages, 5 PS figure
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