The rigid limit in Special Kahler geometry; From K3-fibrations to Special Riemann surfaces: a detailed case study

The limiting procedure of special Kahler manifolds to their rigid limit is studied for moduli spaces of Calabi-Yau manifolds in the neighbourhood of certain singularities. In two examples we consider all the periods in and around the rigid limit, identifying the nontrivial ones in the limit as periods of a meromorphic form on the relevant Riemann surfaces. We show how the Kahler potential of the special Kahler manifold reduces to that of a rigid special Kahler manifold. We extensively make use of the structure of these Calabi-Yau manifolds as K3 fibrations, which is useful to obtain the periods even before the K3 degenerates to an ALE manifold in the limit. We study various methods to calculate the periods and their properties. The development of these methods is an important step to obtain exact results from supergravity on Calabi-Yau manifolds.Comment: 79 pages, 8 figures. LaTeX; typos corrected, version to appear in Classical and Quantum Gravit

Tits-Satake projections of homogeneous special geometries

We organize the homogeneous special geometries, describing as well the couplings of D=6, 5, 4 and 3 supergravities with 8 supercharges, in a small number of universality classes. This relates manifolds on which similar types of dynamical solutions can exist. The mathematical ingredient is the Tits-Satake projection of real simple Lie algebras, which we extend to all solvable Lie algebras occurring in these homogeneous special geometries. Apart from some exotic cases all the other, 'very special', homogeneous manifolds can be grouped in seven universality classes. The organization of these classes, which capture the essential features of their basic dynamics, commutes with the r- and c-map. Different members are distinguished by different choices of the paint group, a notion discovered in the context of cosmic billiard dynamics of non maximally supersymmetric supergravities. We comment on the usefulness of this organization in universality classes both in relation with cosmic billiard dynamics and with configurations of branes and orbifolds defining special geometry backgrounds.Comment: 65 pages, LaTeX; v2: added reference; v3: small corrections, section 3.3 modifie

N=4 Versus N=2 Phases, Hyperk\"Ahler Quotients and the 2D Topological Twist

We consider N=2 and N=4 supersymmetric gauge theories in two-dimensions, coupled to matter multiplets. In analogy with the N=2 case also in the N=4 case one can introduce Fayet-Iliopoulos terms.The associated three-parameters have the meaning of momentum-map levels in a HyperK\"ahler quotient construction. Differently from the N=2 case, however, the N=4 has a single phase corresponding to an effective $\sigma$-model. There is no Landau-Ginzburg phase. The main possible application of our N=4 model is to an effective Lagrangian construction of a $\sigma$-model on ALE-manifolds. We discuss the A and B topological twists of these models clarifying some issues not yet discussed in the literature, in particular the identification of the topological systems emerging from the twist. Applying our results to the case of ALE-manifolds we indicate how one can use the topologically twisted theories to study the K\"ahler class and complex structure deformations of these gravitational instantons.Comment: plain Latex, 77 pages, SISSA/151/93/E

Spinning particles in the vacuum C metric

The motion of a spinning test particle given by the Mathisson-Papapetrou equations is studied on an exterior vacuum C metric background spacetime describing the accelerated motion of a spherically symmetric gravitational source. We consider circular orbits of the particle around the direction of acceleration of the source. The symmetries of this configuration lead to the reduction of the differential equations of motion to algebraic relations. The spin supplementary conditions as well as the coupling between the spin of the particle and the acceleration of the source are discussed.Comment: IOP macros used, eps figures n.

The lightest scalar in theories with broken supersymmetry

We study the scalar mass matrix of general supersymmetric theories with local gauge symmetries, and derive an absolute upper bound on the lightest scalar mass. This bound can be saturated by suitably tuning the superpotential, and its positivity therefore represents a necessary and sufficient condition for the existence of metastable vacua. It is derived by looking at the subspace of all those directions in field space for which an arbitrary supersymmetric mass term is not allowed and scalar masses are controlled by supersymmetry-breaking splitting effects. This subspace includes not only the direction of supersymmetry breaking, but also the directions of gauge symmetry breaking and the lightest scalar is in general a linear combination of fields spanning all these directions. We present explicit results for the simplest case of theories with a single local gauge symmetry. For renormalizable gauge theories, the lightest scalar is a combination of the Goldstino partners and its square mass is always positive. For more general non-linear sigma models, on the other hand, the lightest scalar can involve also the Goldstone partner and its square mass is not always positive.Comment: 30 pages, 3 figures; v2 introduction expanded, paragraph added in section 5 and two references adde

Cesarean delivery on maternal request: Can the ethical problem be solved by the principlist approach?

In this article, we use the principlist approach to identify, analyse and attempt to solve the ethical problem raised by a pregnant woman's request for cesarean delivery in absence of medical indications