74 research outputs found
Extremal Multicenter Black Holes: Nilpotent Orbits and Tits Satake Universality Classes
Four dimensional supergravity theories whose scalar manifold is a symmetric
coset manifold U[D=4]/Hc are arranged into a finite list of Tits Satake
universality classes. Stationary solutions of these theories, spherically
symmetric or not, are identified with those of an euclidian three-dimensional
sigma-model, whose target manifold is a Lorentzian coset U[D=3]/H* and the
extremal ones are associated with H* nilpotent orbits in the K* representation
emerging from the orthogonal decomposition of the algebra U[D=3] with respect
to H*. It is shown that the classification of such orbits can always be reduced
to the Tits-Satake projection and it is a class property of the Tits Satake
universality classes. The construction procedure of Bossard et al of extremal
multicenter solutions by means of a triangular hierarchy of integrable
equations is completed and converted into a closed algorithm by means of a
general formula that provides the transition from the symmetric to the solvable
gauge. The question of the relation between H* orbits and charge orbits W of
the corresponding black holes is addressed and also reduced to the
corresponding question within the Tits Satake projection. It is conjectured
that on the vanishing locus of the Taub-NUT current the relation between
H*-orbit and W-orbit is rigid and one-to-one. All black holes emerging from
multicenter solutions associated with a given H* orbit have the same W-type.
For the S^3 model we provide a complete survey of its multicenter solutions
associated with all of the previously classified nilpotent orbits of sl(2) x
sl(2) within g[2,2]. We find a new intrinsic classification of the W-orbits of
this model that might provide a paradigm for the analogous classification in
all the other Tits Satake universality classes.Comment: 83 pages, LaTeX; v2: few misprints corrected and references adde
The R-map and the Coupling of N=2 Tensor Multiplets in 5 and 4 Dimensions
We study the dimensional reduction of five dimensional N=2
Yang-Mills-Einstein supergravity theories (YMESGT) coupled to tensor
multiplets. The resulting 4D theories involve first order interactions among
tensor and vector fields with mass terms. If the 5D gauge group, K, does not
mix the 5D tensor and vector fields, the 4D tensor fields can be integrated out
in favor of 4D vector fields and the resulting theory is dual to a standard 4D
YMESGT. The gauge group has a block diagonal symplectic embedding and is a
semi-direct product of the 5D gauge group K with a Heisenberg group of
dimension (2P+1), where 2P is the number of tensor fields in five dimensions.
There exists an infinite family of theories, thus obtained, whose gauge groups
are pp-wave contractions of the simple noncompact groups of type SO*(2M). If,
on the other hand, the 5D gauge group does mix the 5D tensor and vector fields,
the resulting 4D theory is dual to a 4D YMESGT whose gauge group does, in
general,NOT have a block diagonal symplectic embedding and involves additional
topological terms. The scalar potentials of the dimensionally reduced theories
naturally have some of the ingredients that were found necessary for stable de
Sitter ground states. We comment on the relation between the known 5D and 4D,
N=2 supergravities with stable de Sitter ground states.Comment: 42 pages;latex fil
E_{7(7)} symmetry and dual gauge algebra of M-theory on a twisted seven-torus
We consider M-theory compactified on a twisted 7-torus with fluxes when all
the seven antisymmetric tensor fields in four dimensions have been dualized
into scalars and thus the E_{7(7)} symmetry is recovered. We find that the
Scherk--Schwarz and flux gaugings define a ``dual'' gauge algebra, subalgbra of
E_{7(7)}, where some of the generators are associated with vector fields which
are dual to part of the original vector fields (deriving from the 3-form). In
particular they are dual to those vector fields which have been ``eaten'' by
the antisymmetric tensors in the original theory by the (anti-)Higgs mechanism.
The dual gauge algebra coincides with the original gauge structure when the
quotient with respect to these dual (broken) gauge generators is taken. The
particular example of the S-S twist corresponding to a ``flat group'' is
considered.Comment: 12 pages, LaTeX file, typos corrected, references added, some
discussions extende
N=2 Supergravity and N=2 Super Yang-Mills Theory on General Scalar Manifolds: Symplectic Covariance, Gaugings and the Momentum Map
The general form of N=2 supergravity coupled to an arbitrary number of vector
multiplets and hypermultiplets, with a generic gauging of the scalar manifold
isometries is given. This extends the results already available in the
literature in that we use a coordinate independent and manifestly symplectic
covariant formalism which allows to cover theories difficult to formulate
within superspace or tensor calculus approach. We provide the complete
lagrangian and supersymmetry variations with all fermionic terms, and the form
of the scalar potential for arbitrary quaternionic manifolds and special
geometry, not necessarily in special coordinates. Lagrangians for rigid
theories are also written in this general setting and the connection with local
theories elucidated. The derivation of these results using geometrical
techniques is briefly summarized.Comment: LaTeX, 80 pages, extended version of hep-th/960300
N=2 supergravity models with stable de Sitter vacua
In the present talk I shall review the construction of N=2 supergravity
models exhibiting stable de Sitter vacua. These solutions represent the first
instance of stable backgrounds with positive cosmological constant in the
framework of extended supergravities (N >=2). After briefly reviewing the role
of de Sitter space--times in inflationary cosmology, I shall describe the main
ingredients which were necessary for the construction of gauged N=2
supergravity models admitting stable solutions of this kind.Comment: Prepared for Workshop on the Quantum Structure of Spacetime and the
Geometric Nature of Fundamental Interactions, Leuven, Belgium, September
13-19 200
Stable de Sitter vacua in N=2, D=5 supergravity
We find 5D gauged supergravity theories exhibiting stable de Sitter vacua.
These are the first examples of stable de Sitter vacua in higher-dimensional
(D>4) supergravity. Non-compact gaugings with tensor multiplets and R-symmetry
gauging seem to be the essential ingredients in these models. They are however
not sufficient to guarantee stable de Sitter vacua, as we show by investigating
several other models. The qualitative behaviour of the potential also seems to
depend crucially on the geometry of the scalar manifold.Comment: 26 pages, v2:typos corrected, published versio
A Search for Non-Perturbative Dualities of Local Yang--Mills Theories from Calabi--Yau Threefolds
The generalisation of the rigid special geometry of the vector multiplet
quantum moduli space to the case of supergravity is discussed through the
notion of a dynamical Calabi--Yau threefold. Duality symmetries of this
manifold are connected with the analogous dualities associated with the
dynamical Riemann surface of the rigid theory. N=2 rigid gauge theories are
reviewed in a framework ready for comparison with the local case. As a
byproduct we give in general the full duality group (quantum monodromy) for an
arbitrary rigid gauge theory, extending previous explicit
constructions for the cases. In the coupling to gravity, R--symmetry
and monodromy groups of the dynamical Riemann surface, whose structure we
discuss in detail, are embedded into the symplectic duality group
associated with the moduli space of the dynamical Calabi--Yau threefold.Comment: Latex. Version of previous paper with enlarged and revised appendix
35 pages, plain LaTe
General Matter Coupled N=2 Supergravity
The general form of N=2 supergravity coupled to an arbitrary number of vector
multiplets and hypermultiplets, with a generic gauging of the scalar manifold
isometries is given. This extends the results already available in the
literature in that we use a coordinate independent and manifestly symplectic
covariant formalism which allows to cover theories difficult to formulate
within superspace or tensor calculus approach. We provide the complete
lagrangian and supersymmetry variations with all fermionic terms, and the form
of the scalar potential for arbitrary quaternionic manifolds and special
geometry, not necessarily in special coordinates. Our results can be used to
explore properties of theories admitting supergravity as low energy
limit.Comment: LaTex, 20 pg
Tits-Satake projections of homogeneous special geometries
We organize the homogeneous special geometries, describing as well the
couplings of D=6, 5, 4 and 3 supergravities with 8 supercharges, in a small
number of universality classes. This relates manifolds on which similar types
of dynamical solutions can exist. The mathematical ingredient is the
Tits-Satake projection of real simple Lie algebras, which we extend to all
solvable Lie algebras occurring in these homogeneous special geometries. Apart
from some exotic cases all the other, 'very special', homogeneous manifolds can
be grouped in seven universality classes. The organization of these classes,
which capture the essential features of their basic dynamics, commutes with the
r- and c-map. Different members are distinguished by different choices of the
paint group, a notion discovered in the context of cosmic billiard dynamics of
non maximally supersymmetric supergravities. We comment on the usefulness of
this organization in universality classes both in relation with cosmic billiard
dynamics and with configurations of branes and orbifolds defining special
geometry backgrounds.Comment: 65 pages, LaTeX; v2: added reference; v3: small corrections, section
3.3 modifie
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