  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 $\BC^2$.
