A Note on Dimer Models and D-brane Gauge Theories

Understand

The connection between quiver gauge theories and dimer models has been well studied.

• It is known that the matter fields of the quiver gauge theories can be represented using the perfect matchings of the corresponding dimer model.We conjecture that a subset of perfect matchings associated with an internal point in the toric diagram is sufficient to give information about the charge matrix of the quiver gauge theory.
• Further, we perform explicit computations on some aspects of partial resolutions of toric singularities using dimer models.
• We analyse these with graph theory techniques, using the perfect matchings of orbifolds of the form $\BC^3/\Gamma$, where the orbifolding group $\Gamma$ may be noncyclic.