Toric Calabi-Yau four-folds dual to Chern-Simons-matter theories

We propose a new method to find gravity duals to a large class of three-dimensional Chern-Simons-matter theories, using techniques from dimer models. The gravity dual is given by M-theory on AdS_4\times Y_7, where Y_7 is an arbitrary seven-dimensional toric Sasaki-Einstein manifold. The cone of Y_7 is a toric Calabi-Yau 4-fold, which coincides with a branch of the vacuum moduli space of Chern-Simons-matter theories.