On the noncommutative Donaldson-Thomas invariants arising from brane tilings

Given a brane tiling, that is it bipartite graph oil it torus, we can associate with it a quiver potential and a quiver potential algebra. Under certain consistency conditions oil it brane tiling, we prove a formula for the Donaldson-Thomas type invariants of the Moduli space of framed cyclic modules over the corresponding quiver potential algebra. We relate this formula with the counting of perfect matchings of the periodic plane tiling corresponding to the brane tiling. We prove that the same consistency conditions imply that the quiver potential algebra is a 3-Calabi-Yau algebra. We also formulate a rationality conjecture for the generating functions of the Donaldson-Thomas type invariants. (C) 2009 Elsevier Inc. All rights reserved.