D-brane stability, geometric engineering, and monodromy in the Derived Category
Abstract
We discuss aspects of topological B-type D-branes in the framework of the derived category of coherent sheaves on a Calabi-Yau 3-fold X. We analyze the link between massless D-branes and monodromies in the CFT moduli space. A classification of all massless D-branes at any point in the moduli space is conjectured, together with an associated monodromy. We test the conjectures in two independent ways. First we establish a composition formula for certain Fourier-Mukai functors, which is a consequence of the triangulated structure of D(X). Secondly, using pi-stability we rederive the stable soliton spectrum of the pure N=2 supersymmetric SU(2) Seiberg-Witten theory. In this approach, the simplicity of the spectrum rests on Grothendieck's theorem concerning vector bundles over P^1.
Cite
@article{arxiv.hep-th/0512343,
title = {D-brane stability, geometric engineering, and monodromy in the Derived Category},
author = {Robert L. Karp},
journal= {arXiv preprint arXiv:hep-th/0512343},
year = {2007}
}
Comments
Talk given at QTS3, 9 pages