Dimer models and toric diagrams

Details Dimer models and toric diagrams Dimer models and toric diagrams

2005-03-19

arxiv.org/abs/hep-th/0503149v2

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, latex2e, JHEP style. v2: corrected typos and added note on fate of 'missing' 18th phase of Y^{6,0}

Scientific paper

We propose a duality between quiver gauge theories and the combinatorics of dimer models. The connection is via toric diagrams together with multiplicities associated to points in the diagram (which count multiplicities of fields in the linear sigma model construction of the toric space). These multiplicities may be computed from both sides and are found to agree in all known examples. The dimer models provide new insights into the quiver gauge theories: for example they provide a closed formula for the multiplicities of arbitrary orbifolds of a toric space, and allow a new algorithmic method for exploring the phase structure of the quiver gauge theory.

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