Exceptional collections and D-branes probing toric singularities

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.

49 pages, 6 figures; v2 refs added; v3 published version

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• The Standard Model Quiver in de Sitter String Compactifications
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• Wall Crossing, Quivers and Crystals
• Deformations of Toric Singularities and Fractional Branes
• Vafa-Witten invariants from exceptional collections
• Quantum Deformations from Toric Geometry
• Global embeddings for branes at toric singularities
• Moduli Spaces for D-branes at the Tip of a Cone
• Branes and instantons intersecting at angles
• Seiberg duality for Chern-Simons quivers and D-brane mutations
• C^2/Z_n Fractional branes and Monodromy
• On the Classification of Duality Webs for Graded Quivers
• Quantum symmetries and exceptional collections