Torsion D-Branes in Nongeometrical Phases

TL;DR

This paper investigates the classification and behavior of torsion D-branes in nongeometrical phases of Calabi-Yau compactifications, providing explicit constructions and insights into their charges in complex string theory backgrounds.

Contribution

It extends the understanding of D-brane charges to nongeometrical phases, explicitly constructing torsion D-branes at the Gepner point in complex Calabi-Yau models.

Findings

Explicit construction of torsion D-branes at the Gepner point.

Evidence for tracking D-brane charges through nongeometrical regions.

Analysis of nonabelian orbifold Gepner models.

Abstract

In a geometrical background, D-brane charge is classified by topological K-theory. The corresponding classification of D-brane charge in an arbitrary, nongeometrical, compactification is still a mystery. We study D-branes on non-simply-connected Calabi-Yau 3-folds, with particular interest in the D-branes whose charges are torsion elements of the K-theory. We argue that we can follow the D-brane charge through the nongeometrical regions of the Kahler moduli space and, as evidence, explicitly construct torsion D-branes at the Gepner point in some examples. In one of our examples, the Gepner theory is a nonabelian orbifold of a tensor product of minimal models, and this somewhat exotic situation seems to be essential to the physics.