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arXiv · hep-th/0507175

Exceptional collections and D-branes probing toric singularities

Christopher P. Herzog·Robert L. Karp
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Abstract

We demonstrate that a strongly exceptional collection on a singular toric surface can be used to derive the gauge theory on a stack of D3-branes probing the Calabi-Yau singularity caused by the surface shrinking to zero size. A strongly exceptional collection, i.e., an ordered set of sheaves satisfying special mapping properties, gives a convenient basis of D-branes. We find such collections and analyze the gauge theories for weighted projective spaces, and many of the Y^{p,q} and L^{p,q,r} spaces. In particular, we prove the strong exceptionality for all p in the Y^{p,p-1} case, and similarly for the Y^{p,p-2r} case.

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Christopher P. Herzog, Robert L. Karp. 2006-03-24. Exceptional collections and D-branes probing toric singularities. https://doi.org/10.1088/1126-6708%2F2006%2F02%2F061

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