Conifold Cosmologies in IIA String Theory

We discuss the extension of our recent work hep-th/0410272, hep-th/0410273 to general conifold transitions and type-IIA string theory.Comment: 8 pages, 4 figures, contributed to the proceedings of the 37-th International Symposium Ahrenshoop, Berlin, August 23-27, 200

Critical Wilson Lines in Toroidal Compactifications of Heteroric Strings

Critical values of Wilson lines and general background fields for toroidal compactifications of heterotic string theories are constructed systematically using Dynkin diagrams.Comment: 32 pages, LATE

Special geometry, black holes and Euclidean supersymmetry

We review recent developments in special geometry and explain its role in the theory of supersymmetric black holes. To make this article self-contained, a short introduction to black holes is given, with emphasis on the laws of black hole mechanics and black hole entropy. We also summarize the existing results on the para-complex version of special geometry, which occurs in Euclidean supersymmetry. The role of real coordinates in special geometry is illustrated, and we briefly indicate how Euclidean supersymmetry can be used to study stationary black hole solutions via dimensional reduction over time. This article is an updated and substantially extended version of the previous review article `New developments in special geometry', hep-th/0602171.Comment: 39 pages, Contribution to the Handbook on Pseudo-Riemannian Geometry and Supersymmtry, ed. V. Corte

Duality and black hole partition functions

Supersymmetric black holes provide an excellent theoretical laboratory to test ideas about quantum gravity in general and black hole entropy in particular. When four-dimensional supergravity is interpreted as the low-energy approximation of ten-dimensional string theory or eleven-dimensional M-theory, one has a microscopic description of the black hole which allows one to count microstates and to compare the result to the macroscopic (geometrical) entropy. Recently it has been conjectured that there is a very direct connection between the partition function of the topological string and a partition function for supersymmetric black holes. We review this idea and propose a modification which makes it compatible with electric-magnetic duality.Comment: 5 pages, based on talk given at the 11th Marcel Grossmann meeting, Berlin, July 23-29, 200

New developments in special geometry

We review recent developments in special geometry, emphasizing the role of real coordinates. In the first part we discuss the para-complex geometry of vector and hypermultiplets in rigid Euclidean N=2 supersymmetry. In the second part we study the variational principle governing the near horizon limit of BPS black holes in matter-coupled N=2 supergravity and observe that the black hole entropy is the Legendre transform of the Hesse potential encoding the geometry of the scalar fields.Comment: 27 pages, contributed to the Handbook on Pseudo-Riemannian Geometry and Supersymmetr

Topological Transitions and Enhancon-like Geometries in Calabi-Yau Compactifications of M-Theory

We study the impact of topological phase transitions of the internal Calabi-Yau threefold on the space-time geometry of five-dimensional extremal black holes and black strings. For flop transitions and SU(2) gauge symmetry enhancement we show that solutions can always be continued and that the behaviour of metric, gauge fields and scalars can be characterized in a model independent way. Then we look at supersymmetric solutions which describe naked singularities rather than geometries with a horizon. For black strings we show that the solution cannot become singular as long as the scalar fields take values inside the Kahler cone. For black holes we establish the same result for the elliptic fibrations over the Hirzebruch surfaces F_0, F_1, F_2. These three models exhibit a behaviour similar to the enhancon, since one runs into SU(2) enhancement before reaching the apparent singularity. Using the proper continuation inside the enhancon radius one finds that the solution is regular.Comment: 7 page

Hessian geometry and the holomorphic anomaly

We present a geometrical framework which incorporates higher derivative corrections to the action of N = 2 vector multiplets in terms of an enlarged scalar manifold which includes a complex deformation parameter. This enlarged space carries a deformed version of special Kahler geometry which we characterise. The holomorphic anomaly equation arises in this framework from the integrability condition for the existence of a Hesse potential.Comment: 43 pages. Revised version: minimal changes. Final version, accepted for publication by JHE