66 research outputs found
Landscape benefits of a forest conversion programme in North East Germany: results of a choice experiment
The article describes the results of a choice experiment aimedat valuing landscape benefits of different kinds of forests in NE Germany by using computer generated images. Preferences for broadleaved/mixed forests over conifers amount to 40-85 ⏠per year and household, additional visual diversity has a monetary value of about 20 âŹ/a. This is true for the summer aspect of forests only. The same experiment conducted with winter images reveals no general preference for broadleaves, whereas visual diversity is valued even higher under winter conditions.The results are part of a study which aimed at valuing the impacts of a regional forest conversionprogramme. Beyond landscape value, the valuation has covered recreational value, the value for climate protection as well as timber production value. The development of landscape values over time can compensate for diminished timber returns until about 2080; afterwards the balance becomes negative. Carbon values are relatively minor in comparison to landscape and timber values
E10 and SO(9,9) invariant supergravity
We show that (massive) D=10 type IIA supergravity possesses a hidden rigid
SO(9,9) symmetry and a hidden local SO(9) x SO(9) symmetry upon dimensional
reduction to one (time-like) dimension. We explicitly construct the associated
locally supersymmetric Lagrangian in one dimension, and show that its bosonic
sector, including the mass term, can be equivalently described by a truncation
of an E10/K(E10) non-linear sigma-model to the level \ell<=2 sector in a
decomposition of E10 under its so(9,9) subalgebra. This decomposition is
presented up to level 10, and the even and odd level sectors are identified
tentatively with the Neveu--Schwarz and Ramond sectors, respectively. Further
truncation to the level \ell=0 sector yields a model related to the reduction
of D=10 type I supergravity. The hyperbolic Kac--Moody algebra DE10, associated
to the latter, is shown to be a proper subalgebra of E10, in accord with the
embedding of type I into type IIA supergravity. The corresponding decomposition
of DE10 under so(9,9) is presented up to level 5.Comment: 1+39 pages LaTeX2e, 2 figures, 2 tables, extended tables obtainable
by downloading sourc
Hidden symmetries and the fermionic sector of eleven-dimensional supergravity
We study the hidden symmetries of the fermionic sector of D=11 supergravity,
and the role of K(E10) as a generalised `R-symmetry'. We find a consistent
model of a massless spinning particle on an E10/K(E10) coset manifold whose
dynamics can be mapped onto the fermionic and bosonic dynamics of D=11
supergravity in the near space-like singularity limit. This E10-invariant
superparticle dynamics might provide the basis of a new definition of M-theory,
and might describe the `de-emergence' of space-time near a cosmological
singularity.Comment: 15 pages, v2: updated references and typos corrected, v3: updated
references and minor correction
An E9 multiplet of BPS states
We construct an infinite E9 multiplet of BPS states for 11D supergravity. For
each positive real root of E9 we obtain a BPS solution of 11D supergravity, or
of its exotic counterparts, depending on two non-compact transverse space
variables. All these solutions are related by U-dualities realised via E9 Weyl
transformations in the regular embedding of E9 in E10, E10 in E11. In this way
we recover the basic BPS solutions, namely the KK-wave, the M2 brane, the M5
brane and the KK6-monopole, as well as other solutions admitting eight
longitudinal space dimensions. A novel technique of combining Weyl reflexions
with compensating transformations allows the construction of many new BPS
solutions, each of which can be mapped to a solution of a dual effective action
of gravity coupled to a certain higher rank tensor field. For real roots of E10
which are not roots of E9, we obtain additional BPS solutions transcending 11D
supergravity (as exemplified by the lowest level solution corresponding to the
M9 brane). The relation between the dual formulation and the one in terms of
the original 11D supergravity fields has significance beyond the realm of BPS
solutions. We establish the link with the Geroch group of general relativity,
and explain how the E9 duality transformations generalize the standard Hodge
dualities to an infinite set of `non-closing dualities'.Comment: 76 pages, 6 figure
IIA and IIB spinors from K(E10)
We analyze the decomposition of recently constructed unfaithful spinor
representations of K(E10) under its SO(9) x SO(9), and SO(9) x SO(2) subgroups,
respectively, where K(E10) is the `maximal compact' subgroup of the hyperbolic
Kac--Moody group E(10). We show that under these decompositions, respectively,
one and the same K(E10) spinor gives rise to both the fermionic fields of IIA
supergravity, and to the (chiral) fermionic fields of IIB supergravity. This
result is thus the fermionic analogue of the decomposition of E(10) under its
SO(9,9) and SL(9) x SL(2) subgroups, respectively, which yield the correct
bosonic multiplets of (massive) IIA and IIB supergravity. The essentially
unique Lagrangian for the supersymmetric E(10)/K(E10) sigma-model therefore can
also capture the dynamics of IIA and IIB including bosons and fermions in the
known truncations.Comment: 16 pages, v2: added paragraph on spinors for K(E9) and K(E11
K(E10), Supergravity and Fermions
We study the fermionic extension of the E10/K(E10) coset model and its
relation to eleven-dimensional supergravity. Finite-dimensional spinor
representations of the compact subgroup K(E10) of E(10,R) are studied and the
supergravity equations are rewritten using the resulting algebraic variables.
The canonical bosonic and fermionic constraints are also analysed in this way,
and the compatibility of supersymmetry with local K(E10) is investigated. We
find that all structures involving A9 levels 0,1 and 2 nicely agree with
expectations, and provide many non-trivial consistency checks of the existence
of a supersymmetric extension of the E10/K(E10) coset model, as well as a new
derivation of the `bosonic dictionary' between supergravity and coset
variables. However, there are also definite discrepancies in some terms
involving level 3, which suggest the need for an extension of the model to
infinite-dimensional faithful representations of the fermionic degrees of
freedom.Comment: 50 page
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
A Parametrization of Bipartite Systems Based on SU(4) Euler Angles
In this paper we give an explicit parametrization for all two qubit density
matrices. This is important for calculations involving entanglement and many
other types of quantum information processing. To accomplish this we present a
generalized Euler angle parametrization for SU(4) and all possible two qubit
density matrices. The important group-theoretical properties of such a
description are then manifest. We thus obtain the correct Haar (Hurwitz)
measure and volume element for SU(4) which follows from this parametrization.
In addition, we study the role of this parametrization in the Peres-Horodecki
criteria for separability and its corresponding usefulness in calculating
entangled two qubit states as represented through the parametrization.Comment: 23 pages, no figures; changed title and abstract and rewrote certain
areas in line with referee comments. To be published in J. Phys. A: Math. and
Ge
E10 and Gauged Maximal Supergravity
We compare the dynamics of maximal three-dimensional gauged supergravity in
appropriate truncations with the equations of motion that follow from a
one-dimensional E10/K(E10) coset model at the first few levels. The constant
embedding tensor, which describes gauge deformations and also constitutes an
M-theoretic degree of freedom beyond eleven-dimensional supergravity, arises
naturally as an integration constant of the geodesic model. In a detailed
analysis, we find complete agreement at the lowest levels. At higher levels
there appear mismatches, as in previous studies. We discuss the origin of these
mismatches.Comment: 34 pages. v2: added references and typos corrected. Published versio
Consistent truncation of d = 11 supergravity on AdS_4 x S^7
We study the system of equations derived twenty five years ago by B. de Wit
and the first author [Nucl. Phys. B281 (1987) 211] as conditions for the
consistent truncation of eleven-dimensional supergravity on AdS_4 x S^7 to
gauged N = 8 supergravity in four dimensions. By exploiting the E_7(7)
symmetry, we determine the most general solution to this system at each point
on the coset space E_7(7)/SU(8). We show that invariants of the general
solution are given by the fluxes in eleven-dimensional supergravity. This
allows us to both clarify the explicit non-linear ansatze for the fluxes given
previously and to fill a gap in the original proof of the consistent
truncation. These results are illustrated with several examples.Comment: 41 pages, typos corrected, published versio
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