Three families of tilting mutations on brane tilings produce quiver-invariant dualities, linking five doublets and one triplet of toric phases of H^{1,1,2,1}.
Brane Tilings and Exceptional Collections
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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.
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Tilting Mutations and Quiver-Invariant Dualities in Brane Tilings
Three families of tilting mutations on brane tilings produce quiver-invariant dualities, linking five doublets and one triplet of toric phases of H^{1,1,2,1}.