Towards M2-brane Theories for Generic Toric Singularities

Understand

We construct several examples of (2+1) dimensional N=2 supersymmetric Chern-Simons theories, whose moduli space is given by non-compact toric Calabi-Yau four-folds, which are not derivable from any (3+1) dimensional CFT.

• One such example is the gauge theory associated with the cone over Q^{111}.
• For several examples, we explicitly confirm the matter content, superpotential interactions and RG flows suggested by crystal models.
• Our results provide additional support to the idea that crystal models are relevant for describing the structure of these CFTs.