Supersymmetric Three-cycles and (Super)symmetry Breaking

TL;DR

This paper explores how transitions in supersymmetric three-cycles within Calabi-Yau threefolds influence supersymmetry breaking and BPS state evolution in string theory, revealing mechanisms for spontaneous gauge and supersymmetry breaking.

Contribution

It introduces a detailed analysis of supersymmetric three-cycle transitions in Calabi-Yau manifolds and their role in supersymmetry breaking in type IIB and IIA string theories.

Findings

Transitions occur at real codimension one in moduli space.

BPS states become degenerate with non-supersymmetric states at transition points.

D6-brane wrapping cycles realize Fayet models with spontaneous symmetry breaking.

Abstract

We describe physical phenomena associated with a class of transitions that occur in the study of supersymmetric three-cycles in Calabi-Yau 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 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 non-supersymmetric 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.