Brane Tilings and Exceptional Collections
arXiv:hep-th/0602041 · doi:10.1088/1126-6708/2006/07/001
Abstract
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.
46 pages, 37 figures, JHEP3; v2: reference added, figure 13 corrected
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- Crystal Melting and Black Holes
- Non-perturbative effects and wall-crossing from topological strings
- New Example of Infinite Family of Quiver Gauge Theories
- Metastable vacua and geometric deformations