On Dimer Models and Closed String Theories

We study some aspects of the recently discovered connection between dimer models and D-brane gauge theories. We argue that dimer models are also naturally related to closed string theories on non compact orbifolds of $\BC^2$ and $\BC^3$, via their twisted sector R charges, and show that perfect matchings in dimer models correspond to twisted sector states in the closed string theory. We also use this formalism to study the combinatorics of some unstable orbifolds of $\BC^2$.