Towards M2-brane Theories for Generic Toric Singularities

TL;DR

This paper constructs new (2+1)D N=2 supersymmetric Chern-Simons theories with moduli spaces as non-compact toric Calabi-Yau four-folds, not obtainable from 3+1D CFTs, supporting the relevance of crystal models.

Contribution

It provides explicit examples of such theories, confirming their matter content, superpotentials, and RG flows, thus advancing understanding of M2-brane theories for toric singularities.

Findings

Confirmed matter content and superpotentials for new theories

Validated RG flow patterns consistent with crystal models

Supported the relevance of crystal models for these CFTs

Abstract

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.