Abstract

We discuss a class of three-dimensional N = 4 Chern-Simons (CS) quiver gauge models obtained from M-theory compactifications on singular complex four-dimensional hyper-Kahler (HK) manifolds, which are realized explicitly as a cotangent bundle over two-Fano toric varieties V-2. The corresponding CS gauge models are encoded in quivers similar to toric diagrams of V-2. Using toric geometry, it is shown that the constraints on CS levels can be related to toric equations determining V-2.