On the Higgsing and UnHiggsing of Fano 3-Folds

TL;DR

This paper explores the Higgsing and UnHiggsing processes in M2-brane theories probing toric Fano 3-folds, revealing new gauge theories and analyzing their geometric and combinatorial properties.

Contribution

It introduces new M2-brane gauge theories, including those not associated with Fano cones, and provides insights into quiver theories with varied external point multiplicities.

Findings

Discovered new M2-brane gauge theories via brane tilings.

Identified examples of theories without tiling descriptions.

Analyzed Higgsing of a CY 4-fold without a tiling.

Abstract

We study the Higgsing and UnHiggsing of M2-brane theories that probe cones over smooth toric Fano 3-folds, via brane tilings. We find many new examples of M2-brane gauge theories not studied previously in the literature, including those that do not correspond to cones over Fano varieties. Our analysis also provides, upon unHiggsing the known Fano varieties, new examples of quiver gauge theories that describe the same toric variety, but with external point multiplicities. As a byproduct of our results, we discuss an example of a CY 4-fold that does not have a tiling description, and study the Higgsing of this theory.