Perturbative and non-perturbative monodromies in N=2 heterotic string vacua

In this talk we summarise our recent results on perturbative and non-perturbative monodromies in four-dimensional heterotic strings with $N=2$ space-time supersymmetry, and we compare our results with the rigid $SU(2)$ $N=2$ Yang-Mills monodromies.Comment: 6 pages, latex using espcrc2. Based on Talks given at the 29th International Symposium on the Theory of Elementary Particles, Buckow, August 1995 and at the 5th Hellenic School and Workshop on Elementary Particle Physics, Corfu, September 199

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

Natural Supergravity Inflation

We show that a single uncharged chiral superfield, canonically coupled to \mbox{$N=1$} supergravity with vanishing superpotential, naturally drives inflation in the early universe for a class of simple Kahler potentials. Inflation occurs due to the one-loop generation of a Kahler anomaly proportional to $\R^2$. The coefficient of this $\R^2$ term is of the correct magnitude to describe all aspects of an inflationary cosmology, including sufficient amplitude perturbations and reheating. Higher order terms proportional to $\R^n$ for $n \geq 3$ are naturally suppressed relative to the $\R^2$ term and, hence, do not destabilize the theory.Comment: 13 pages, CERN-TH.6685/92, UPR-0526

Duality Symmetries and Supersymmetry Breaking in String Compactifications

We discuss the spontaneous supersymetry breaking within the low-energy effective supergravity action of four-dimensional superstrings. In particular, we emphasize the non-universality of the soft supersymmetry breaking parameters, the $\mu$-problem and the duality symmetries.Comment: (invited talk to the 27th ICHEP, Glasgow, July 1994), 11 page

Curved BPS domain wall solutions in five-dimensional gauged supergravity

We analyze the possibility of constructing supersymmetric curved domain wall solutions in five-dimensional ${\cal N}=2$ gauged supergravity, which are supported by non-constant scalar fields belonging either to vector multiplets only or to vector and hypermultiplets. We show that the BPS equations for the warp factor and for the vector scalars are modified by the presence of a four-dimensional cosmological constant on the domain wall, in agreement with earlier results by DeWolfe, Freedman, Gubser and Karch. We also show that the cosmological constant on the domain wall is anti-de Sitter like and that it constitutes an independent quantity, not related to any of the objects appearing in the context of very special geometry.Comment: 13 pages, latex, error corrected plus substantial revision (title changed

Indefinite theta functions for counting attractor backgrounds

In this note, we employ indefinite theta functions to regularize canonical partition functions for single-center dyonic BPS black holes. These partition functions count dyonic degeneracies in the Hilbert space of four-dimensional toroidally compactified heterotic string theory, graded by electric and magnetic charges. The regularization is achieved by viewing the weighted sums of degeneracies as sums over charge excitations in the near-horizon attractor geometry of an arbitrarily chosen black hole background, and eliminating the unstable modes. This enables us to rewrite these sums in terms of indefinite theta functions. Background independence is then implemented by using the transformation property of indefinite theta functions under elliptic transformations, while modular transformations are used to make contact with semi-classical results in supergravity.Comment: 24 pages, LaTe

Supersymmetric Solutions in Three-Dimensional Heterotic String Theory

We consider the low-energy effective field theory of heterotic string theory compactified on a seven-torus, and we construct electrically charged as well as more general solitonic solutions. These solutions preserve 1/2, 1/4 and 1/8 of N=8, D=3 supersymmetry and have Killing spinors which exist due to cancellation of holonomies. The associated space-time line elements do not exhibit the conical structure that often arises in 2+1 dimensional gravity theories.Comment: 40 pages, LaTeX, minor correction