Superconformal field theories from M-theory crystal lattices

We propose a brane configuration for the (2+1)d, N=2 superconformal theories (CFT₃) arising from M2 branes probing toric Calabi-Yau 4-fold cones, using a T-duality transformation of M theory. We obtain intersections of M5-branes on a three-torus which form a 3d bipartite crystal lattice in a way similar to the 2d dimer models for CFT₄. The fundamental fields of the CFT₃ are M2-brane discs localized around the intersections, and the superpotential terms are identified with the atoms of the crystal. The model correctly reproduces the Bogomol'nyi-Prasad-Sommerfield (BPS) spectrum of mesons.