  The 2d (0,2) supersymmetric gauge theories corresponding to the classes of
Y^{p,k}(CP^1 x CP^1) and Y^{p,k}(CP^2) manifolds are identified. The complex
cones over these Sasaki-Einstein 7-manifolds are non-compact toric Calabi-Yau
4-folds. These infinite families of geometries are the largest ones for
Sasaki-Einstein 7-manifolds whose metrics, toric diagrams, and volume functions
are known explicitly. This work therefore presents the largest classification
of 2d (0,2) supersymmetric gauge theories corresponding to Calabi-Yau 4-folds
with known metrics.
