589 research outputs found
The Complete Form of N=2 Supergravity and its Place in the General Framework of D=4 N--Extended Supergravities
Relying on the geometrical set up of Special K\"ahler Geometry and
Quaternionic Geometry, which I discussed at length in my Lectures at the 1995
edition of this Spring School, I present here the recently obtained fully
general form of N=2 supergravity with completely arbitrary couplings. This
lagrangian has already been used in the literature to obtain various results:
notably the partial breaking of supersymmetry and various extremal black--hole
solutions. My emphasis, however, is only on providing the reader with a
completely explicit and ready to use component expression of the supergravity
action. All the details of the derivation are omitted but all the definitions
of the items entering the lagrangian and the supersymmetry transformation rules
are given.Comment: 11 pages, LaTeX espcrc2, Seminar at Trieste Spring School 199
The full integration of black hole solutions to symmetric supergravity theories
We prove that all stationary and spherical symmetric black hole solutions to
theories with symmetric target spaces are integrable and we provide an explicit
integration method. This exact integration is based on the description of black
hole solutions as geodesic curves on the moduli space of the theory when
reduced over the time-like direction. These geodesic equations of motion can be
rewritten as a specific Lax pair equation for which mathematicians have
provided the integration algorithms when the initial conditions are described
by a diagonalizable Lax matrix. On the other hand, solutions described by
nilpotent Lax matrices, which originate from extremal regular (small) D = 4
black holes can be obtained as suitable limits of solutions obtained in the
diagonalizable case, as we show on the generating geodesic (i.e. most general
geodesic modulo global symmetries of the D = 3 model) corresponding to regular
(and small) D = 4 black holes. As a byproduct of our analysis we give the
explicit form of the Wick rotation connecting the orbits of BPS and non-BPS
solutions in maximally supersymmetric supergravity and its STU truncation.Comment: 27 pages, typos corrected, references added, 1 figure added,
Discussion on black holes and the generating geodesic significantly extended.
Statement about the relation between the D=3 geodesics from BPS and non-BPS
extreme black holes made explicit by defining the Wick rotation mapping the
corresponding orbit
On the Gauged Kahler Isometry in Minimal Supergravity Models of Inflation
In this paper we address the question how to discriminate whether the gauged
isometry group G_Sigma of the Kahler manifold Sigma that produces a D-type
inflaton potential in a Minimal Supergravity Model is elliptic, hyperbolic or
parabolic. We show that the classification of isometries of symmetric cosets
can be extended to non symmetric Sigma.s if these manifolds satisfy additional
mathematical restrictions. The classification criteria established in the
mathematical literature are coherent with simple criteria formulated in terms
of the asymptotic behavior of the Kahler potential K(C) = 2 J(C) where the real
scalar field C encodes the inflaton field. As a by product of our analysis we
show that phenomenologically admissible potentials for the description of
inflation and in particular alpha-attractors are mostly obtained from the
gauging of a parabolic isometry, this being, in particular the case of the
Starobinsky model. Yet at least one exception exists of an elliptic
alpha-attractor, so that neither type of isometry can be a priori excluded. The
requirement of regularity of the manifold Sigma poses instead strong
constraints on the alpha-attractors and reduces their space considerably.
Curiously there is a unique integrable alpha-attractor corresponding to a
particular value of this parameter.Comment: 85 pages, LaTex, 32 jpg figures, 4 tables; v2: title and abstract
slightly modified, some assessments improved and made more precise, two
figures and one reference added, several misprints correcte
Global U(1) R-Symmetry And Conformal Invariance Of (0,2) Models
We derive a condition under which (0,2) linear sigma models possess a
``left-moving'' conformal stress tensor in \bq cohomology (i.e. which leaves
invariant the ``right-moving'' ground states) even away from their critical
points. At the classical level this enforces quasihomogeneity of the
superpotential terms. The persistence of this structure at the quantum level on
the worldsheet is obstructed by an anomaly unless the charges and
superpotential degrees satisfy a condition which is equivalent to the condition
for the cancellation of the anomaly in a particular ``right-moving'' U(1)
R-symmetry.Comment: 8 page
Integrability of Supergravity Black Holes and New Tensor Classifiers of Regular and Nilpotent Orbits
In this paper we apply in a systematic way a previously developed integration
algorithm of the relevant Lax equation to the construction of spherical
symmetric, asymptotically flat black hole solutions of N=2 supergravities with
symmetric Special Geometry. Our main goal is the classification of these
black-holes according to the H*-orbits in which the space of possible Lax
operators decomposes, H* being the isotropy group of scalar manifold
originating from time-like dimensional reduction of supergravity from D=4 to
D=3 dimensions. The main result of our investigation is the construction of
three universal tensors, extracted from quadratic and quartic powers of the Lax
operator, that are capable of classifying both regular and nilpotent H* orbits
of Lax operators. Our tensor based classification is compared, in the case of
the simple one-field model S^3, to the algebraic classification of nilpotent
orbits and it is shown to provide a simple and practical discriminating method.
We present a detailed analysis of the S^3 model and its black hole solutions,
discussing the Liouville integrability of the corresponding dynamical system.
By means of the Kostant-representation of a generic Lie algebra element, we
were able to develop an algorithm which produces the necessary number of
hamiltonians in involution required by Liouville integrability of generic
orbits. The degenerate orbits correspond to extremal black-holes and are
nilpotent. We analyze these orbits in some detail working out different
representatives thereof and showing that the relation between H* orbits and
critical points of the geodesic potential is not one-to-one. Finally we present
the conjecture that our newly identified tensor classifiers are universal and
able to label all regular and nilpotent orbits in all homogeneous symmetric
Special Geometries.Comment: Analysis of nilpotent orbits in terms of tensor classifiers in
section 8.1 corrected. Table 1 corrected. Discussion in section 11 extende
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