Brane Tilings and Exceptional Collections

Details Brane Tilings and Exceptional Collections Brane Tilings and Exceptional Collections

2006-02-05

arxiv.org/abs/hep-th/0602041v2

JHEP0607:001,2006

Physics

High Energy Physics

High Energy Physics - Theory

46 pages, 37 figures, JHEP3; v2: reference added, figure 13 corrected

Scientific paper

10.1088/1126-6708/2006/07/001

Both brane tilings and exceptional collections are useful tools for describing the low energy gauge theory on a stack of D3-branes probing a Calabi-Yau singularity. We provide a dictionary that translates between these two heretofore unconnected languages. Given a brane tiling, we compute an exceptional collection of line bundles associated to the base of the non-compact Calabi-Yau threefold. Given an exceptional collection, we derive the periodic quiver of the gauge theory which is the graph theoretic dual of the brane tiling. Our results give new insight to the construction of quiver theories and their relation to geometry.

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