On the vacuum structure of type II string compactifications on Calabi-Yau spaces with H-fluxes

We discuss the vacuum structure of type IIA/B Calabi-Yau string compactific ations to four dimensions in the presence of n-form H-fluxes. These will li ft the vacuum degeneracy in the Calabi-Yau moduli space, and for generic po ints in the moduli space, N = 2 supersymmetry will be broken. However, for certain 'aligned' choices of the H-flux vector, supersymmetric ground state s are possible at the degeneration points of the Calabi-Yau geometry. We wi ll investigate in detail the H-flux induced superpotential and the correspo nding scalar potential at several degeneration points, such as the Calabi-Y au large volume limit, the conifold loci, the Seiberg-Witten points, the st rong coupling point and the conformal points. Some emphasis is given to the question whether partial supersymmetry breaking can be realized at those p oints. We also relate the H-flux induced superpotential to the formalism of gauged Ar = 2 supergravity. Finally, we point out the analogies between th e Calabi-Yau vacuum structure due to H-fluxes and the attractor formalism o f Ar = 2 black holes. (C) 2001 Published by Elsevier Science B.V.