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 $(b,c,\beta,\gamma)$-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 $E_\rightarrow {\cal M}_g$, whose sections are the holomorphic differentials. Its complex dimension is $2g-3$, rather then $3g-3$. 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 $c=6$, instead of the value $c=9$ 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 $\sigma$-model. There is no Landau-Ginzburg phase. The main possible application of our N=4 model is to an effective Lagrangian construction of a $\sigma$-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