74 research outputs found
Cosmic Billiards with Painted Walls in Non-Maximal Supergravities: a worked out example
The derivation of smooth cosmic billiard solutions through the compensator
method is extended to non maximal supergravities. A new key feature is the
non-maximal split nature of the scalar coset manifold. To deal with this, one
needs the theory of Tits Satake projections leading to maximal split projected
algebras. Interesting exact solutions that display several smooth bounces can
thus be derived. From the analysis of the Tits Satake projection emerges a
regular scheme for all non maximal supergravities and a challenging so far
unobserved structure, that of the paint group G-paint. This latter is preserved
through dimensional reduction and provides a powerful tool to codify solutions.
It appears that the dynamical walls on which the cosmic ball bounces come
actually in painted copies rotated into each other by G-paint. The effective
cosmic dynamics is that dictated by the maximal split Tits Satake manifold plus
paint. We work out in details the example provided by N=6,D=4 supergravity,
whose scalar manifold is the special Kahlerian SO*(12)}/SU(6)xU(1). In D=3 it
maps to the quaternionic E_7(-5)/ SO(12) x SO(3). From this example we extract
a scheme that holds for all supergravities with homogeneous scalar manifolds
and that we plan to generalize to generic special geometries. We also comment
on the merging of the Tits-Satake projection with the affine Kac--Moody
extensions originating in dimensional reduction to D=2 and D=1.Comment: 52 pages, 4 figures, 9 tables, paper. Few misprints correcte
Black holes as D3-branes on Calabi-Yau threefolds
We show how an extremal Reissner-Nordstrom black hole can be obtained by
wrapping a dyonic D3-brane on a Calabi-Yau manifold. In the orbifold limit
T^6/Z_3, we explicitly show the correspondence between the solution of the
supergravity equations of motion and the D-brane boundary state description of
such a black hole.Comment: 14 pages, LaTex, minor corrections, version to appear on Phys. Lett.
Elliptic Genera and N=2 Superconformal Field Theory
Recently Witten proposed to consider elliptic genus in superconformal
field theory to understand the relation between minimal models and
Landau-Ginzburg theories. In this paper we first discuss the basic properties
satisfied by elliptic genera in theories. These properties are confirmed
by some fundamental class of examples. Then we introduce a generic procedure to
compute the elliptic genera of a particular class of orbifold theories, {\it
i.e.\/} the ones orbifoldized by in the Neveu-Schwarz sector.
This enables us to calculate the elliptic genera for Landau-Ginzburg orbifolds.
When the Landau-Ginzburg orbifolds allow an interpretation as target manifolds
with holonomy we can compare the expressions with the ones obtained by
orbifoldizing tensor products of minimal models. We also give sigma model
expressions of the elliptic genera for manifolds of holonomy.Comment: 24 pages, harvmac (citation corrected, reference added
Twisted N=2 Supergravity as Topological Gravity in Four Dimensions
We show that the BRST quantum version of pure D=4 N=2 supergravity can be
topologically twisted, to yield a formulation of topological gravity in four
dimensions. The topological BRST complex is just a rearrangement of the old
BRST complex, that partly modifies the role of physical and ghost fields:
indeed, the new ghost number turns out to be the sum of the old ghost number
plus the internal U(1) charge. Furthermore, the action of N=2 supergravity is
retrieved from topological gravity by choosing a gauge fixing that reduces the
space of physical states to the space of gravitational instanton
configurations, namely to self-dual spin connections. The descent equations
relating the topological observables are explicitly exhibited and discussed.
Ours is a first step in a programme that aims at finding the topological sector
of matter coupled N=2 supergravity, viewed as the effective Lagrangian of type
II superstrings and, as such, already related to 2D topological field-theories.
As it stands the theory we discuss may prove useful in describing gravitational
instantons moduli-spaces.Comment: 38 page
The rigid limit in Special Kahler geometry; From K3-fibrations to Special Riemann surfaces: a detailed case study
The limiting procedure of special Kahler manifolds to their rigid limit is
studied for moduli spaces of Calabi-Yau manifolds in the neighbourhood of
certain singularities. In two examples we consider all the periods in and
around the rigid limit, identifying the nontrivial ones in the limit as periods
of a meromorphic form on the relevant Riemann surfaces. We show how the Kahler
potential of the special Kahler manifold reduces to that of a rigid special
Kahler manifold. We extensively make use of the structure of these Calabi-Yau
manifolds as K3 fibrations, which is useful to obtain the periods even before
the K3 degenerates to an ALE manifold in the limit. We study various methods to
calculate the periods and their properties. The development of these methods is
an important step to obtain exact results from supergravity on Calabi-Yau
manifolds.Comment: 79 pages, 8 figures. LaTeX; typos corrected, version to appear in
Classical and Quantum Gravit
Gauged Hyperinstantons and Monopole Equations
The monopole equations in the dual abelian theory of the N=2 gauge-theory,
recently proposed by Witten as a new tool to study topological invariants, are
shown to be the simplest elements in a class of instanton equations that follow
from the improved topological twist mechanism introduced by the authors in
previous papers. When applied to the N=2 sigma-model, this twisting procedure
suggested the introduction of the so-called hyperinstantons, or triholomorphic
maps. When gauging the sigma-model by coupling it to the vector multiplet of a
gauge group G, one gets gauged hyperinstantons that reduce to the
Seiberg-Witten equations in the flat case and G=U(1). The deformation of the
self-duality condition on the gauge-field strength due to the
monopole-hyperinstanton is very similar to the deformation of the self-duality
condition on the Riemann curvature previously observed by the authors when the
hyperinstantons are coupled to topological gravity. In this paper the general
form of the hyperinstantonic equations coupled to both gravity and gauge
multiplets is presented.Comment: 13 pages, latex, no figures, [revision: a couple of references
reordered correctly
Topological First-Order Systems with Landau-Ginzburg Interactions
We consider the realization of N=2 superconformal models in terms of free
first-order -systems, and show that an arbitrary
Landau-Ginzburg interaction with quasi-homogeneous potential can be introduced
without spoiling the (2,2)-superconformal invariance. We discuss the
topological twisting and the renormalization group properties of these
theories, and compare them to the conventional topological Landau-Ginzburg
models. We show that in our formulation the parameters multiplying deformation
terms in the potential are flat coordinates. After properly bosonizing the
first-order systems, we are able to make explicit calculations of topological
correlation functions as power series in these flat coordinates by using
standard Coulomb gas techniques. We retrieve known results for the minimal
models and for the torus.Comment: 37 page
N=8 supersymmetric mechanics on special K\"ahler manifolds
We propose the Hamiltonian model of supersymmetric mechanics on
dimensional special K\"ahler manifolds (of the rigid type).Comment: 4 page
Special geometry and symplectic transformations
Special Kahler manifolds are defined by coupling of vector multiplets to
supergravity. The coupling in rigid supersymmetry exhibits similar
features. These models contain vectors in rigid supersymmetry and in
supergravity, and complex scalars. Apart from exceptional cases they are
defined by a holomorphic function of the scalars. For supergravity this
function is homogeneous of second degree in an -dimensional projective
space. Another formulation exists which does not start from this function, but
from a symplectic - or -dimensional complex space. Symplectic
transformations lead either to isometries on the manifold or to symplectic
reparametrizations. Finally we touch on the connection with special
quaternionic and very special real manifolds, and the classification of
homogeneous special manifolds.Comment: 11 pages, latex using espcrc2, no figures. Some factors and minor
corrections. Version to be published in the proceedings of the Spring
workshop on String theory, Trieste, April 199
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