D-Brane Stability and Monodromy

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.

35 pages, 8 figures, refs added

References in corpus (9)

• Derived Categories and Zero-Brane Stability
• Split attractor flows and the spectrum of BPS D-branes on the Quintic
• Enhanced D-Brane Categories from String Field Theory
• Unitarity, D-brane dynamics and D-brane categories
• Derived Category Automorphisms from Mirror Symmetry
• D-Branes and N=1 Supersymmetry
• Boundary Fermions, Coherent Sheaves and D-branes on Calabi-Yau manifolds
• Some Navigation Rules for D-Brane Monodromy
• A new kind of McKay correspondence from non-Abelian gauge theories

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