Partial Resolution of Complex Cones over Fano ℬ

Abstract EN

In our recent paper, we systematized an inverse algorithm to obtain quiver gauge theory living on the M2-branes probing the singularities of a special kind of Calabi-Yau fourfold which were complex cones over toric Fano ℙ3, ℬ1, ℬ2, ℬ3.

These quiver gauge theories cannot be given a dimer tiling presentation.

We use the method of partial resolution to show that the toric data of ℂ4 and Fano ℙ3 can be embedded inside the toric data of Fano ℬ theories.

This method indirectly justifies that the two-node quiver Chern-Simons theories corresponding to ℂ4, Fano ℙ3, and their orbifolds can be obtained by higgsing matter fields of the three-node parent quiver corresponding to Fano ℬ1, ℬ2, ℬ3, ℬ4 threefold.