Klaus Behrndt

Non-extreme black holes of five-dimensional N = 2 AdS supergravity

Abstract We consider static black holes of D = 5, N = 2 gauged supergravity with general spatial curvature k and show that the modifications due to the gauging as well as k enter only the non-extremality function. Therefore, one can promote any (known) black hole solution of ungauged supergravity with k = +1 to a solution of gauged supergravity with an arbitrary k . As an example we discuss a solution for the STU model of gauged supergravity which is incidentally also a solution of D = 5 N = 4 and N = 8 gauged supergravity. This solution is specified by three charges, the asymptotic negative cosmological constant (minimum of the potential) and a non-extremality parameter. While its BPS-saturated limit has a naked singularity, we find a lower bound on the non-extremality parameter (or equivalently on the ADM mass) for which the non-extreme solutions are regular. When this bound is saturated the extreme (non-supersymmetric) solution has zero Hawking temperature and finite entropy. Analogous qualitative features are expected to emerge for black hole solutions in D = 4 gauged supergravity as well.

STATIONARY SOLUTIONS OF N = 2 SUPERGRAVITY

Abstract We discuss general bosonic stationary configurations of N = 2, D = 4 supergravity coupled to vector multiplets. The requirement of unbroken supersymmetries imposes constraints on the holomorphic symplectic section of the underlying special Kahler manifold. The corresponding solutions of the field equations are completely determined by a set of harmonic functions. As examples we discuss rotating black holes, Taub-NUT and Eguchi-Hanson-like instantons for the STU model. In addition, we discuss, in the static limit, world-sheet instanton corrections to the STU black hole solution, in the neighborhood of a vanishing 4-cycle of the Calabi-Yau manifold. Our procedure is quite general and includes all known black hole solutions that can be embedded into N = 2 supergravity.

STU black holes and string triality

We found double-extreme black holes associated with the special geometry of the Calabi-Yau moduli space with the prepotential F = STU. The area formula is STU-moduli independent and has [SL(2, Z)]{sup 3} symmetry in space of charges. The dual version of this theory without prepotential treats the dilaton S asymmetric versus T,U-moduli. We display the dual relation between new (STU) black holes and stringy (S|TU) black holes using particular Sp(8,Z) transformation. The area formula of one theory equals the area formula of the dual theory when expressed in terms of dual charges. We analyze the relation between (STU) black holes to string triality of black holes: (S|TU), (T|US), (U|ST) solutions. In democratic STU-symmetric version we find that all three S and T and U duality symmetries are non-perturbative and mix electric and magnetic charges.

BPS black holes in N=2 five dimensional ADS supergravity

Abstract BPS black hole solutions of U (1) gauged five-dimensional supergravity are obtained by solving the Killing spinor equations. These extremal static black holes live in an asymptotic AdS 5 space time. Unlike black holes in asymptotic flat space time none of them possess a regular horizon. We also calculate the influence, of a particular class of these solutions, on the Wilson loops calculation.

General N = 1 Supersymmetric Fluxes in (Massive) Type IIA String Theory

Abstract We study conditions on general fluxes of massive type IIA supergravity that lead to four-dimensional backgrounds with N = 1 supersymmetry. We derive these conditions in the case of SU ( 3 ) - as well as SU ( 2 ) -structures. SU ( 3 ) -structures imply that the internal space is constrained to be a nearly Kahler manifold with all the turned on fluxes, and the negative cosmological constant proportional to the mass parameter, and the dilaton fixed by the quantized ratio of the three-form and four-form fluxes. We further discuss the implications of such flux vacua with added intersecting D6-branes, leading to the chiral non-Abelian gauge sectors (without orientifold projections). Examples that break SU ( 3 ) -structures to SU ( 2 ) -ones allow for the internal space conformally flat (up to orbifold and orientifold projections), for which we give an explicit example. These results provide a starting point for further study of the four-dimensional (chiral) N = 1 supersymmetric solutions of massive type IIA supergravity with D-branes and fluxes, compactified on orientifolds.

Domain walls and superpotentials from M-theory on Calabi–Yau three-folds

Compactification of M-theory in the presence of G-fluxes yields N = 2 five-dimensional gauged supergravity with a potential that lifts all supersymmetric vacua. We derive the effective superpotential directly from the Kaluza–Klein reduction of the eleven-dimensional action on a Calabi–Yau three-fold and compare it with the superpotential obtained by means of calibrations. We discuss an explicit domain wall solution, which represents five-branes wrapped over holomorphic cycles. This solution has a “running volume” and we comment on the possibility that quantum corrections provide a lower bound allowing for an AdS5 vacuum of the 5-dimensional supergravity.

Anti-de Sitter vacua of gauged supergravities with 8 supercharges

We investigate supersymmetric extrema of Abelian gauged supergravity theories with nontrivial vector multiplets and 8 supercharges in four and five dimensions. The scalar fields of these models parametrize a manifold consisting of disconnected branches and, restricting to the case where this manifold has a nonsingular metric, we show that on every branch there can be at most one extremum, which is a local maximum (for W>0) or a minimum (for W<0) of the superpotential W. Therefore, these supergravity models do not allow for regular domain wall solutions interpolating between different extrema of the superpotential and the space-time transverse to the wall asymptotically always approaches the boundary of AdS (UV-fixed points in a dual field theory). (c) 2000 The American Physical Society.

Higher-order black-hole solutions in N=2 supergravity and Calabi-Yau string backgrounds

Abstract Based on special geometry, we consider corrections to N=2 extremal black-hole solutions and their entropies originating from higher-order derivative terms in N=2 supergravity. These corrections are described by a holomorphic function, and the higher-order black-hole solutions can be expressed in terms of symplectic Sp(2n+2) vectors. We apply the formalism to N=2 type-IIA Calabi-Yau string compactifications and compare our results to recent related results in the literature.

About a class of exact string backgrounds

Abstract We investigate a class of string backgrounds which have one conserved chiral null current on the world sheet. In the target space they have a null Killing vector and unbroken supersymmetries. This class also known as the chiral null model is a generalization of the gravitational wave and fundamental string background and is exact in the α′ expansion. The reduction to 4 dimensions yields a stationary IWP solution which couples to 7 gauge fields (one gravi-photon and 6 matter gauge fields) and 4 scalars. Special cases are the Taub-NUT geometry and rotating black holes. These solutions possess a T-self-dual point where the black hole becomes massless. Discussing the S-duality we show that the Taub-NUT geometry allows an S-self-dual point and that the electric black hole corresponds to a magnetic black hole or an H-monopole. We could identify the massless black hole as N L = 0 and confirm the H-monopole as an N L = 1 string state.

Exploring the relation between 4D and 5D BPS solutions

Abstract Based on recent proposals linking four and five-dimensional BPS solutions, we discuss the explicit dictionary between general stationary 4D and 5D supersymmetric solutions in N = 2 supergravity theories with cubic prepotentials. All these solutions are completely determined in terms of the same set of harmonic functions and the same set of attractor equations. As an example, we discuss black holes and black rings in Godel–Taub-NUT spacetime. Then we consider corrections to the 4D solutions associated with more general prepotentials and comment on analogous corrections on the 5D side.