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

Euclidean Actions, Instantons, Solitons and Supersymmetry

Theories with axionic scalars admit three different Euclidean formulations, obtained by Wick rotation, Wick rotation combined with analytic continuation of the axionic scalars, and Wick rotation combined with Hodge dualization. We investigate the relation between these formulations for a class of theories which contains the sigma models of N=2 vector multiplets as a special case. It is shown that semi-classical amplitudes can be expressed equivalently using the two types of axionic actions, while the Hodge dualized version gives a different value for the instanton action unless the integration constants associated with the axion fields are chosen in a particular way. With this choice the instanton action is equal to the mass of the soliton or black hole obtained by dimensional lifting with respect to time. For supersymmetric models we use the Euclidean supersymmetry algebra to derive a Euclidean BPS condition, and we identify a geometrical criterion which distinguishes BPS from non-BPS extremal solutions.Comment: 38 page

Effective Supergravity Actions for Conifold Transitions

We construct gauged supergravity actions which describe the dynamics of M-theory on a Calabi-Yau threefold in the vicinity of a conifold transition. The actions explicitly include N charged hypermultiplets descending from wrapped M2-branes which become massless at the conifold point. While the vector multiplet sector can be treated exactly, we approximate the hypermultiplet sector by the non-compact Wolf spaces X(1+N). The effective action is then uniquely determined by the charges of the wrapped M2-branes.Comment: 57 pages, no figure

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

Excision of singularities by stringy domain walls

We study supersymmetric domain walls on S1/Z2 orbifolds. The supergravity solutions in the bulk are given by the attractor equation associated with Calabi–Yau (CY) spaces and have a naked space–time singularity at some |ys|. We are looking for possibilities to cut off this singularity with the second wall by a stringy mechanism. We use the collapse of the CY cycle at |yc| which happens before and at a finite distance from the space–time singularity. In our example with three Kähler moduli the second wall is at the end of the moduli space at |yc| where also the enhancement of SU(2) gauge symmetry takes place so that |ye| = |yc|1/R duality. The position of the enhançon is given by the equation R(|ye|) = 1

Singular compactifications and cosmology

We summarize our recent results of studying five-dimensional Kasner cosmologies in a time-dependent Calabi-Yau compactification of M-theory undergoing a topological flop transition. The dynamics of the additional states, which become massless at the transition point and give rise to a scalar potential, helps to stabilize the moduli and triggers short periods of accelerated cosmological expansion.Comment: 4 pages; contribution to the proceedings of the EURESCO conference "What comes beyond the Standard Model?", July 2003, Portoroz, Sloveni