A Note on Dimer Models and D-brane Gauge Theories

Abstract

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 $\BC^3/Γ$, where the orbifolding group $\Gamma$ may be noncyclic. Using these, we study the construction of the superpotential of gauge theories living on D-branes which probe these singularities, including the case where one or more adjoint fields are present upon partial resolution. Applying a combination of open and closed string techniques to dimer models, we also study some aspects of their symmetries.

Discussions expanded, clarifications added, typos fixed. 1+49 pages

References in corpus (7)

• Dimer models and toric diagrams
• Brane Tilings
• The Master Space of N=1 Gauge Theories
• An introduction to the dimer model
• Gauge Theories at Resolved and Deformed Singularities using Dimers
• Moduli Spaces of Gauge Theories from Dimer Models: Proof of the Correspondence
• On Dimer Models and Closed String Theories

Cited by in corpus (7)

• Tilings, Chern-Simons Theories and M2 Branes
• M2-Branes and Quiver Chern-Simons: A Taxonomic Study
• Inverse algorithm and M2-brane theories
• Is toric duality a Seiberg-like duality in (2+1)-d ?
• On the Higgsing and UnHiggsing of Fano 3-Folds
• Partial resolution of complex cones over Fano $\mathcal{B}$
• Embedding and partial resolution of complex cones over Fano threefolds