Superconformal field theories from crystal lattices

TL;DR

This paper introduces a novel brane configuration model for 3-dimensional superconformal field theories derived from M2-branes, utilizing a T-duality approach to relate M-theory brane intersections to crystal lattice structures.

Contribution

It presents a new geometric framework connecting M2-brane theories with 3d bipartite crystal lattices, extending the analogy of dimer models from 4d to 3d CFTs.

Findings

Reproduces the full BPS spectrum of mesons and baryons.

Establishes a correspondence between superpotential terms and crystal atoms.

Provides a geometric interpretation of 3d superconformal theories from M-theory.

Abstract

We propose a brane configuration for the (2+1)d, $\mathcal{N}=2$ superconformal theories (CFT$_3$) 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 CFT$_4$. The fundamental fields of the CFT$_3$ are M2-brane discs localized around the intersections, and the super-potential terms are identified with the atoms of the crystal. The model correctly reproduces the complete BPS spectrum of mesons and baryons.