Exceptional collections and D-branes probing toric singularities | Zendy

Christopher P. Herzog | Zendy; Robert L. Karp | Zendy

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Exceptional collections and D-branes probing toric singularities

Author(s) -

Christopher P. Herzog,

Robert L. Karp

Publication year - 2006

Publication title -

journal of high energy physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.998

H-Index - 261

eISSN - 1126-6708

pISSN - 1029-8479

DOI - 10.1088/1126-6708/2006/02/061

Subject(s) - singularity , gravitational singularity , stack (abstract data type) , gauge (firearms) , mathematics , brane cosmology , surface (topology) , pure mathematics , gauge theory , toric variety , projective test , mathematical physics , mathematical analysis , geometry , computer science , archaeology , history , programming language

We demonstrate that a strongly exceptional collection on a singular toricsurface can be used to derive the gauge theory on a stack of D3-branes probingthe Calabi-Yau singularity caused by the surface shrinking to zero size. Astrongly exceptional collection, i.e., an ordered set of sheaves satisfyingspecial mapping properties, gives a convenient basis of D-branes. We find suchcollections and analyze the gauge theories for weighted projective spaces, andmany of the Y^{p,q} and L^{p,q,r} spaces. In particular, we prove the strongexceptionality for all p in the Y^{p,p-1} case, and similarly for theY^{p,p-2r} case.Comment: 49 pages, 6 figures; v2 refs added; v3 published versio

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