D-Branes on Vanishing del Pezzo Surfaces

Details D-Branes on Vanishing del Pezzo Surfaces D-Branes on Vanishing del Pezzo Surfaces

2004-05-14

arxiv.org/abs/hep-th/0405134v2

JHEP0412:042,2004

Physics

High Energy Physics

High Energy Physics - Theory

32 pages, several xy-pic figures, typos and minor errors fixed, section 4.3 removed due to possible errors

Scientific paper

10.1088/1126-6708/2004/12/042

We analyze in detail the case of a marginally stable D-Brane on a collapsed del Pezzo surface in a Calabi-Yau threefold using the derived category of quiver representations and the idea of aligned gradings. We show how the derived category approach to D-branes provides a straight-forward and rigorous construction of quiver gauge theories associated to such singularities. Our method shows that a procedure involving exceptional collections used elsewhere in the literature is only valid if some tachyon-inducing Ext3 groups are zero. We then analyze in generality a large class of Seiberg dualities which arise from tilting equivalences. It follows that some (but not all) mutations of exceptional collections induce Seiberg duality in this context. The same tilting equivalence can also be used to remove unwanted Ext3 groups and convert an unphysical quiver into a physical one.

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