Moving Moduli, Calabi-Yau Phase Transitions and Massless BPS Configurations in Type II Superstrings

Abstract

In this paper we discuss compactifications of type II superstrings where the moduli of the internal Calabi-Yau space vary over four-dimensional space time. The corresponding solutions of four-dimensional N=2 supergravity are given by charged, extremal BPS black hole configurations with non-constant scalar field values. In particular we investigate the behaviour of our solutions near those points in the Calabi-Yau moduli space where some internal cycles collapse and topology change (flop transitions, conifold transitions) can take place. The singular loci in the internal space are related to special points in the uncompactified space. The phase transition can happen either at spatial infinity (for positive charges) or on spheres (with at least one negative charge). The corresponding BPS configuration has zero ADM mass and can be regarded as a domain wall that separates topologically different vacua of the theory.

Figures (1)

• Figure 1: This figure shows the Calabi-Yau space varying over the three-dimensional space. In type IIB strings, at the conifold point some 3-cycles of the Calabi-Yau space vanish and are replaced by topologically different cycles. We argue, that this happens on $S_2$ spheres in space time where harmonic functions vanish. These spheres can be seen as domain walls that separate topological different vacua.