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D-brane stability, geometric engineering, and monodromy in the Derived Category

Robert L. Karp
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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.

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Robert L. Karp. 2005-12-29. D-brane stability, geometric engineering, and monodromy in the Derived Category. https://arxiv.org/abs/hep-th/0512343

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