Brane tilings and exceptional collections | Zendy

Amihay Hanany | Zendy; Christopher P. Herzog | Zendy; David Vegh | Zendy

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Brane tilings and exceptional collections

Author(s) -

Amihay Hanany,

Christopher P. Herzog,

David Vegh

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 - 10.1088/1126-6708/2006/07/001

Subject(s) - quiver , brane , singularity , gauge theory , theoretical physics , stack (abstract data type) , brane cosmology , physics , gauge (firearms) , singularity theory , mathematics , pure mathematics , geometry , mathematical physics , computer science , geography , archaeology , programming language

Both brane tilings and exceptional collections are useful tools fordescribing the low energy gauge theory on a stack of D3-branes probing aCalabi-Yau singularity. We provide a dictionary that translates between thesetwo heretofore unconnected languages. Given a brane tiling, we compute anexceptional collection of line bundles associated to the base of thenon-compact Calabi-Yau threefold. Given an exceptional collection, we derivethe periodic quiver of the gauge theory which is the graph theoretic dual ofthe brane tiling. Our results give new insight to the construction of quivertheories and their relation to geometry.Comment: 46 pages, 37 figures, JHEP3; v2: reference added, figure 13 correcte

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