New gravitational solutions via a Riemann-Hilbert approach

We consider the Riemann-Hilbert factorization approach to solving the field equations of dimensionally reduced gravity theories. First we prove that functions belonging to a certain class possess a canonical factorization due to properties of the underlying spectral curve. Then we use this result, together with appropriate matricial decompositions, to study the canonical factorization of non-meromorphic monodromy matrices that describe deformations of seed monodromy matrices associated with known solutions. This results in new solutions, with unusual features, to the field equations.Comment: 29 pages, 2 figures; v2: reference added, matches published versio

BPS Action and Superpotential for Heterotic String Compactifications with Fluxes

We consider N =1 compactifications to four dimensions of heterotic string theory in the presence of fluxes. We show that up to order O(\alpha'^2) the associated action can be written as a sum of squares of BPS-like quantities. In this way we prove that the equations of motion are solved by backgrounds which fulfill the supersymmetry conditions and the Bianchi identities. We also argue for the expression of the related superpotential and discuss the radial modulus stabilization for a class of examples.Comment: LaTeX, 28 pages. Minor changes, one more reference added. Final version to appear on JHE

Heterotic String Theory on non-Kaehler Manifolds with H-Flux and Gaugino Condensate

We discuss compactifications of heterotic string theory to four dimensions in the presence of H-fluxes, which deform the geometry of the internal manifold, and a gaugino condensate which breaks supersymmetry. We focus on the compensation of the two effects in order to obtain vacua with zero cosmological constant and we comment on the effective superpotential describing these vacua.Comment: 6 page

On Quantum Special Kaehler Geometry

We compute the effective black hole potential V of the most general N=2, d=4 (local) special Kaehler geometry with quantum perturbative corrections, consistent with axion-shift Peccei-Quinn symmetry and with cubic leading order behavior. We determine the charge configurations supporting axion-free attractors, and explain the differences among various configurations in relations to the presence of ``flat'' directions of V at its critical points. Furthermore, we elucidate the role of the sectional curvature at the non-supersymmetric critical points of V, and compute the Riemann tensor (and related quantities), as well as the so-called E-tensor. The latter expresses the non-symmetricity of the considered quantum perturbative special Kaehler geometry.Comment: 1+43 pages; v2: typo corrected in the curvature of Jordan symmetric sequence at page 2

Deformations of special geometry: in search of the topological string

The topological string captures certain superstring amplitudes which are also encoded in the underlying string effective action. However, unlike the topological string free energy, the effective action that comprises higher-order derivative couplings is not defined in terms of duality covariant variables. This puzzle is resolved in the context of real special geometry by introducing the so-called Hesse potential, which is defined in terms of duality covariant variables and is related by a Legendre transformation to the function that encodes the effective action. It is demonstrated that the Hesse potential contains a unique subsector that possesses all the characteristic properties of a topological string free energy. Genus $g\leq3$ contributions are constructed explicitly for a general class of effective actions associated with a special-K\"ahler target space and are shown to satisfy the holomorphic anomaly equation of perturbative type-II topological string theory. This identification of a topological string free energy from an effective action is primarily based on conceptual arguments and does not involve any of its more specific properties. It is fully consistent with known results. A general theorem is presented that captures some characteristic features of the equivalence, which demonstrates at the same time that non-holomorphic deformations of special geometry can be dealt with consistently.Comment: 44 pages, LaTex; v2, v3: minor text improvement

How Does a Fundamental String Stretch its Horizon?

It has recently been shown that if we take into account a class of higher derivative corrections to the effective action of heterotic string theory, the entropy of the black hole solution representing elementary string states correctly reproduces the statistical entropy computed from the degeneracy of elementary string states. So far the form of the solution has been analyzed at distance scales large and small compared to the string scale. We analyze the solution that interpolates between these two limits and point out a subtlety in constructing such a solution due to the presence of higher derivative terms in the effective action. We also study the T-duality transformation rules to relate the moduli fields of the effective field theory to the physical compactification radius in the presence of higher derivative corrections and use these results to find the physical radius of compactification near the horizon of the black hole. The radius approaches a finite value even though the corresponding modulus field vanishes. Finally we discuss the non-leading contribution to the black hole entropy due to space-time quantum corrections to the effective action and the ambiguity involved in comparing this result to the statistical entropy.Comment: LaTeX file, 38 pages; v2: minor changes and added reference

Effective action for the field equations of charged black holes

In this article, we consistently reduce the equations of motion for the bosonic N = 2 supergravity action, using a multi-centered black hole ansatz for the metric. This reduction is done in a general, non-supersymmetric setup, in which we extend concepts of BPS black hole technology. First of all we obtain a more general form of the black hole potential, as part of an effective action for both the scalars and the vectors in the supergravity theory. Furthermore, we show that there are extra constraints specifying the solution, which we calculate explicitly. In the literature, these constraints have already been studied in the one-center case. We also show that the effective action we obtain for non-static metrics, can be linked to the "entropy function" for the spherically symmetric case, as defined by Sen and Cardoso et al.Comment: 18 pages, (v2: small corrections, version to be published in CQG