We describe physical phenomena associated with a class of transitions that occur in the study of supersymmetric three-cycles in Calabi-Yau (CY) threefolds. The transitions in question occur at real codimension one in the complex structure moduli space of the Calabi-Yau manifold. In type-IIB string theory, these transitions can be used to describe the evolution of a Bogomol’nyi-Prasad-Sommerfeld (BPS) state as one moves through a locus of marginal stability: at the transition point the BPS particle becomes degenerate with a supersymmetric two-particle state, and after the transition the lowest energy state carrying the same charges is a nonsupersymmetric two-particle state. In the IIA theory, wrapping the cycles in question with D6 branes leads to a simple realization of the Fayet model: for some values of the CY modulus gauge symmetry is spontaneously broken, while for other values supersymmetry is spontaneously broken.

• Received 17 September 1999

DOI:https://doi.org/10.1103/PhysRevD.61.026001