26 research outputs found
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.
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
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
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
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
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
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
Constrained Topological Gravity from Twisted N=2 Liouville Theory
In this paper we show that there exists a new class of topological field
theories, whose correlators are intersection numbers of cohomology classes in a
constrained moduli space. Our specific example is a formulation of 2D
topological gravity. The constrained moduli-space is the Poincare' dual of the
top Chern-class of the bundle , whose sections are
the holomorphic differentials. Its complex dimension is , rather then
. We derive our model by performing the A-topological twist of N=2
supergravity, that we identify with N=2 Liouville theory, whose rheonomic
construction is also presented. The peculiar field theoretical mechanism,
rooted in BRST cohomology, that is responsible for the constraint on moduli
space is discussed, the key point being the fact that the graviphoton becomes a
Lagrange multiplier after twist. The relation with conformal field theories is
also explored. Our formulation of N=2 Liouville theory leads to a
representation of the N=2 superconformal algebra with , instead of the
value that is obtained by untwisting the Verlinde and Verlinde
formulation of topological gravity. The reduced central charge is the shadow,
in conformal field theory, of the constraint on moduli space.Comment: 48 pages, LaTex file, SISSA 49/94/EP, IFUM 468/F
N=4 Versus N=2 Phases, Hyperk\"Ahler Quotients and the 2D Topological Twist
We consider N=2 and N=4 supersymmetric gauge theories in two-dimensions,
coupled to matter multiplets. In analogy with the N=2 case also in the N=4 case
one can introduce Fayet-Iliopoulos terms.The associated three-parameters have
the meaning of momentum-map levels in a HyperK\"ahler quotient construction.
Differently from the N=2 case, however, the N=4 has a single phase
corresponding to an effective -model. There is no Landau-Ginzburg
phase. The main possible application of our N=4 model is to an effective
Lagrangian construction of a -model on ALE-manifolds. We discuss the A
and B topological twists of these models clarifying some issues not yet
discussed in the literature, in particular the identification of the
topological systems emerging from the twist. Applying our results to the case
of ALE-manifolds we indicate how one can use the topologically twisted theories
to study the K\"ahler class and complex structure deformations of these
gravitational instantons.Comment: plain Latex, 77 pages, SISSA/151/93/E