D-Brane Stability and Monodromy

TL;DR

This paper reviews Pi-stability of B-type D-branes on Calabi-Yau manifolds, emphasizing the role of derived category axioms, and explores monodromy and stability lines with applications to supersymmetry breaking.

Contribution

It demonstrates the importance of the octahedral axiom in stability analysis and derives a conjecture relating monodromy to derived categories in Calabi-Yau contexts.

Findings

Lines of marginal stability are plotted for the quintic Calabi-Yau.

The octahedral axiom is shown to be crucial for understanding D-brane stability.

A conjecture on monodromy around conifold points is formulated.

Abstract

We review the idea of Pi-stability for B-type D-branes on a Calabi-Yau manifold. It is shown that the octahedral axiom from the theory of derived categories is an essential ingredient in the study of stability. Various examples in the context of the quintic Calabi-Yau threefold are studied and we plot the lines of marginal stability in several cases. We derive the conjecture of Kontsevich, Horja and Morrison for the derived category version of monodromy around a "conifold" point. Finally, we propose an application of these ideas to the study of supersymmetry breaking.